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D'Alessandro, Flavio
Free groups of quaternions
Internat. J. Algebra Comput. 14(2004), No.1, 69-86
Abstract: Free subgroups in the multiplicative group of the skewfield of the real quaternions. Tits-like alternative.
Daboul, Claudia and Daboul, Jamil and Montigny, Marc de
Gradings and contractions of affine Kac-Moody algebras
DOI: 10.1063/1.2940318
J. Math. Phys. 49, 063509 (2008)
Daboul, J and Delbourgo, R
Matrix representation of octonions and generalizations
J. Math. Phys. 40 (1999), 4134-4150
hep-th/9906065
Dahl, Geir and Leinaas, Jon Magne and Myrheim, Jan and Ovrum, Eirik
A tensor product matrix approximation problem in quantum physics
DOI: 10.1016/j.laa.2006.08.026
Lin. Algebra Appl. 420 (2007), N2-3, 711-725
Description: Approximation problem of positive semidifenite matrices with trace 1 by so-called separable matrices (decomposable as certain tensor product).
Availability: sdarticle-1.pdf
Dahlberg, Randall P.
Infinite extensions of simple modules over semisimple Lie algebras
Rings, Extensions and Cohomology (ed. A.Magid), Lect. Notes Pure Appl. Math, M.Dekker, 159(1994), 67-
Availability: google print; ext.tar (first 6 pages only)
Daily, Marilyn
L-infinity structures on spaces of low dimension
PhD Thesis, North Carolina State Univ., 2004, 82 pages
Dalalyan, S. G.
The generalized Jordan matrix of a linear operator
Mat. Zametki 82 (2007), no. 1, 27--35
Description: Generalized Jordan normal form over arbitrary field.
Availability: Obobshchenie4.pdf
Daletskii, Yuri L. and Kushnirevitch, Vitaly A.
Formal differential geometry and Nambu-Takhtajan algebra
(ed. R. Budzynski et al.), Quantum groups and quantum spaces, Banach Cent. Publ. 40 (1997), 293-302 (1997)
Zentralblatt: 0883.17029
Description: de Rham complex for (graded) Lie superalgebra and module over it.
Differential structures in Lie superalgebras
Ukr. Math. J. 48 (1996), No.4, 483-490
Ukr. Mat. Zh. 48 (1996), No.4, 435-442
Zentralblatt: 0893.58009
Description: Within the framework of abstract Lie superalgebras, the authors introduce some notions similar to the main objects of differential geometry. In particular, analogues of Hamiltonian operators and a series of brackets are constructed. The latter correspond to the classical Poisson, Schouten and Nijenhuis brackets.
Daletskii, Yuri L. and Takhtajan, Leon A.
Leibniz and Lie Algebra Structures for Nambu Algebra
Letters in Mathematical Physics 39 (2): 127-141, January 1997
Abstract: We canonically associate a Leibniz algebra with every Nambu algebra. We show how various homological and cohomological complexes for a Nambu algebra can be naturally obtained from its structure as a module over the Leibniz algebra. We also present a generalization of a classical Lie--Berezin construction for Nambu algebras and extend these results for Nambu superalgebras.
Dali, Bechir
Linear family of Lie brackets on the space of matrices Mat(n x m,K) and Ado's theorem
arXiv:0807.1851
Description: Classification of Lie algebra structures defined on the space of rectangular matrices of the form [a,b] = axb - bxa. In the case of square matrices, these Lie algebras are contractions of gl(n). (Done, essentially, long time ago - see excerpt from the book by Trofimov-Fomenko).
Dallmer, Elke (nee Mundt)
On Lie Algebras All Nilpotent Subalgebras of Which Are Abelian.
J. Math. Phys. 40(1999), N.8, 4151-4156
Damaskinskii, E.V. and Kulish, P.P.
Deformed oscillators and their applications (in Russian)
Zapiski Nauchn Sem. LOMI, 1991, 37-74
Availability: 1991-deformed-oscillators.djvu
Damian, Erika
Loop Lie algebras which are sl2(C)-modules
PhD Dissertation, Univ. Trento, 2003
Description: Number of generators vs. number of relations, in the spirit of Golod-Shafarevich, Koch and Wisliceny.
Dana-Picard, Thierry
Classifying generic algebras
PhD Thesis, Bar-Ilan U., 1990, 148 pp.
Description: (Algebro-geometric) variety of associative algebra structures, deformations.
Availability: hardcopy (in books)
Dana-Picard, T. and Schaps, M.
Non reduced components of Alg$_n$
Algebras and Modules II (Edited by: Idun Reiten, Sverre O. Smalø, and Øyvind Solberg), CMS Conf. Proc. 24 (1998)
Danilov, A.N.
On the Magnus representation for nonassociative algebras
Vestnik MGU 2003, N2, 50-52
Description: Matrix representation of relatively free algebras which are factoralgebras by monomial ideals (particularly, of relatively free nilpotent and solvable algebras).
Danilov, V I and Koshevoi, G A (=Koshevoy)
Arrays and the combinatorics of Young tableaux
DOI: 10.1070/RM2005v060n02ABEH000824
Russ. Math. Surv. 60 (2005), 269-334
MR 2152944
Zentralblatt: 1081.05104
Abstract: The classical theory of Young tableaux is presented in the rather new and non-traditional language of arrays. With the usual operations (or algorithms) of insertion and jeu de taquin as a starting point, more elementary operations on arrays are introduced. The set of arrays equipped with these operations forms an object which can be referred to as a bicrystal. This formalism is presented in the first part of the paper, and its exposition is based on the theorem that the vertical and horizontal operators commute. In the second part the apparatus of arrays is used to present some topics in the theory of Young tableaux, namely, the plactic monoid, Littlewood-Richardson rule, Robinson-Schensted-Knuth correspondence, dual tableaux, plane partitions, and so on.
Availability: 2005-arrays.pdf
The Robinson-Schensted-Knuth correspondence and the bijections of commutativity and associativity
Izv. Math. 72 (2008), 689-716
Availability: 2008-robinson.pdf
Daniyarova, E. Yu. and Kazatchkov, I. V. and Remeslennikov, V. N.
Algebraic geometry over free metabelian Lie algebra. I. U-algebras and universal classes
Fund. Appl. Math 9(2003), N3, 37-63
Journal of Mathematical Sciences Volume 135, Number 5 June 2006 Pages: 3292 - 3310
Algebraic geometry over free metabelian Lie algebra. II. The finite field case
Fund. Appl. Math. 9(2003), N3, 65-87
Journal of Mathematical Sciences Volume 135, Number 5 June 2006 Pages: 3311 - 332
Semidomains and metabelian product of metabelian Lie algebras
J. Math. Sci. 131(2005), N6, 6015 - 6022
Description: Continuation of previous papers.
Daniyarova, E. and Myasnikov, A. and Remeslennikov, V.
Unification theorems in algebraic geometry
arXiv:0808.2522
Description: Embeddings into ultraproducts, limit algebras.
Daniyarova, E. Yu. and Remeslennikov, V. N.
Bounded Algebraic Geometry over a Free Lie Algebra
Algebra and Logic Volume 44, Number 3 May 2005 Pages: 148 - 167
Dardié, Jean-Michel and Médina, Alberto
Algèbres de Lie kählériennes et double extension
DOI: 10.1006/jabr.1996.0350
J. Alg. 185 (1996), 774-795
Description: Lie algebras having a nondegenerate 2-cocycle. Lie algebars possessing a map j:L->L satisfying [jx,jy] - [x,y] - j[jx,y] - [jx,y] = 0.
Darp\"o, Erik
Normal forms for the G_2-action on the real symmetric 7x7-matrices by conjugation
DOI: 10.1016/j.jalgebra.2007.03.007
arXiv:math.RA/0703321
Journal of Algebra Volume 312, Issue 2, 15 June 2007, Pages 668-688
Abstract: The exceptional Lie group G_2 acts on the set of real symmetric 7x7-matrices by conjugation. We solve the normal form problem for this group action. In view of earlier results, this gives rise to a classification of all finite-dimensional real flexible division algebras.
Darpö, Erik and Dieterich, Ernst
Real Commutative Division Algebras
DOI: 10.1007/s10468-006-9040-3
Algebras and Representation Theory Volume 10, Number 2 / April, 2007 Pages 179-196
Das, Ashish Kumar
On normal subgroups of product of groups
math.GR/0504097
Description: Criterion when all normal subgroups of a direct product of two groups are direct product of their normal subgroups.
Dauben, Joseph W.
Abraham Robinson
Princeton Univ. Press, 1995; paperback, 559 pp.
Availability: hardcopy
Marx, Mao and mathematics: the politics of infinitesimals
Documenat Math., Extra Volume ICM III (1998), 799-809
Description: Nonstandard analysis as ideological tool in China.
Dauns, J.
A Concrete Approach to Division Rings
URL: http://www.ams.org/bull/1984-11-01/S0273-0979-1984-15277-7/S0273-0979-1984-15277-7.pdf http://projecteuclid.org/euclid.bams/1183551852
Heldermann Verlag, 1982; paperback, 417 pp.
Availability: hardcopy (book) ; absent on amazon
Modules and Rings
Cambridge Univ. Press, 1994; hardcover with dustjacket, 442 pp.
Availability: hardcopy (book)
Davis, M.
Engines of Logic
W.W. Norton & Co., New York - London, 2000; paperback, 257 pp.
Description: This is a very entertaining historical account of logical ideas which shaped the modern computing, revolving around such personalities as Leibniz, Boole, Frege, Cantor, Goedel, von Neumann, and Turing, and entities like ENIAC, EDVAC, and Mark I. Sometimes I didn't quite follow the author's (own) logic - for example, it remains unclear what is exactly the place of the Cantor diagonal procedure or Goedel incompletness theorem in the whole picture. So, for me, this was more a collection of essays centered around the unifying theme, than one gradually unfolding story. Sometimes, when author ventures into the ungratifying task of explaining mathematics to a broad audience, it goes a bit boring. Full of historical anecdotes, which often complement and provide different perspective of what I already knew about that or another person from other sources.
Availability: hardcopy (book)
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Davydov, A.
Cohomology of crossed algebras
Noncommutative Geometry and Representation Theory in Mathematical Physics, Contemp. Math. 391 (2005), 41-
Availability: Google print; crossed.tar (first 3 pages only)
De Concini, Corrado and Kac, Victor G.
Representations of quantum groups at roots of 1
Operator Algebras, Unitary Representations, Enveloping Algebras, and Invariant Theory (eds. A.Connes et al.), Birkhauser, 1990, 471-506
Availability: hardcopy
De Concini, C. and Kac, V.G. and Procesi, C.
Quantum coadjoint actions
JAMS 5(1992), N1, 151-189
Availability: hardcopy
Guise, Hubert de and Montigny, Marc de
Graded contractions of Lie algebras and central extensions
Preprint CRM-2626, November 1999
De Loera, Jesús A. and McAllister, Tyrrell B.
On the computation of Clebsch-Gordan coefficients and the dilation effect
Experimental Math. 15 (2006), N1
Description: I don't really understand what is going on there, but it is something charmig.
De Silva, V. and Ghrist, R.
Coordinate-free coverage in sensor networks with controlled boundaries via homology
URL: http://pages.pomona.edu/~vds04747/public/publications.html http://comptop.stanford.edu/preprints/
Int. J. Robotics Research 25 (2006), N12, 1205-1222
Coverage in sensor networks via persistent homology
URL: http://pages.pomona.edu/~vds04747/public/publications.html http://comptop.stanford.edu/preprints/
Algebraic & Geometric Topology 7 (2007), 339-358
De Smedt, Vivian
Existence of a Lie bialgebra structure on every Lie algebra
DOI: 10.1007/BF00761714
Lett. Math. Phys. 31 (1994), N3, 225-231
Zentralblatt: 0797.16045
Description: They are all of the form x \wedge y for certain x,y. Considered various cases from the Levi-Malcev decomposition.
Availability: liebialgebra.latex; 1994-existence.pdf (published version)
De Visscher, Maud
Extensions of modules for SL(2,K)
J. Algebra 254 (2002), no. 2, 409--421
Description: Cohomology of the first Frobenius kernel of SL(2,K) (p>0) in some tensor products.
Availability: science.pdf; hardcopy
De Wilde, M. and Lecomte, P. B. A.
Cohomologie 3-diffe'rentiable de l'alge`bre de Poisson d'une varie'te' symplectique
Ann. Inst. Fourier 33 (1983), no. 4, 83--94
Zentralblatt: 0511.58040
Description: H^2,3(L,L). Highly analytical considerations.
Availability: hardcopy
Existence of star-products and of formal deformations of the Poisson Lie algebra of arbitrary symplectic manifolds
DOI: 10.1007/BF00402248
Lett. Math. Phys. 7 (1983), N6, 487-496
Availability: lmp-1983.pdf
Crochet de Nijenhuis-Richardson et cohomologie de l'alge`bre de Poisson
C. R. Acad. Sci. Paris 300 (1985), no. 1, 9--12
Availability: hardcopy
De Wilde, M. and Lecomte, P. and Gutt, S.
A propos des deuxie`me et troisie`me espaces de cohomologie de l'alge`bre de Lie de Poisson d'une varie'te' symplectique
Ann. Inst. H. Poincare' Sect. A (N.S.) 40 (1984), no. 1, 77--83
Decker, W. and Lossen, C.
Computing in algebraic geometry: A quick start using SINGULAR
Springer, 2006
Availability: Kolkhoz
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Dedecker, P.
Les foncteuers Ext_P, H2^2_P and H^2_P non abeliens
C. R. Acad. Sci. Paris 258 (1964), 4891-4895
Description: "Nonabelian" cohomology describing nonabelian group extensions.
Three-dimensional non-abelian cohomology for groups
Category Theory Homology Theory Appl., Seattle Res. Center Battelle Memorial Inst. 1968(1969?), 2, 32-64
Dedecker, Paul and Lue, Abraham S.-T.
A nonabelian two-dimensional cohomology for associative algebras
Bull. Amer. Math. Soc. 72 (1966), 1044-1050
Zentralblatt: 0156.25903
Availability: hardcopy
Deguchi, Tetsuo
The six-vertex model at roots of unity and some highest weight representations of the ${\rm sl}_2$ loop algebra
Ann. Henri Poincare 7 (2006), no. 7-8, 1531--1540
DEKIMPE, K.
Solvable Lie Algebras, Lie Groups and Polynomial Structures
DOI: 10.1023/A:1001738932743
Compositio Mathematica, Volume 121, Number 2, April 2000 , pp. 183-204(22)
Description: Decomposition of solvable Lie algebars into the sum of two nilpotent subalgebras. Proposition 2.1. Let L be a nilpotent Lie algebra, and M is a finite-dimensional module. If H^0(L,M) = 0 then H^*(L,M) = 0. (this was proved earlier by Dixmier).
Availability: S0010437X00000178a.pdf
Dekimpe, Karel and Igodt, Paul and Pouseele, Hannes
Expanding automorphisms and affine structures on nilpotent Lie algebras with few generators
Comm. Algebra 31(2003), N12, 5847 - 5874
Description: Affine structures on a Lie algebra are closely related to left-symmetric structures.
Availability: affine.pdf
del Olmo, M. A. and Rodriguez, M. A. and Winternitz, P. and Zassenhaus, H.
Maximal abelian subalgebras of pseudounitary Lie algebras
DOI: 10.1016/0024-3795(90)90117-U
Linear Algebra Appl. 135 (1990), 79-151
Availability: 1990-maximal.pdf
Deligne, P. et al.
Quantum Fields and Strings: A Course For Mathematicians
2 vols., AMS, 1999
Description: Including super-Brauer group (Deligne)
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Deligne, P. and Griffiths, P. and Morgan, J. and Sullivan, D.
Real homotopy theory of Kahler manifolds
Inv. Math. 29 (1975), 245-274
Availability: hardcopy
Deligne, Pierre and Leites, Dmitry
Howe's correspondence and superalgberas
Preprint
Description: Semiinfinite cohomology
Availability: HoweDL.{tex,dvi}
Delius, Gustav W. and Gould, Mark D.
Quantum Lie algebras, their existence, uniqueness and q-antisymmetry
Comm. Math. Phys. 185(1997), 709-722
Abstract: Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules $\lqlie$ of the quantized enveloping algebras $\uqg$. On them the quantum Lie product is given by the quantum adjoint action. Here we define for any finite-dimensional simple complex Lie algebra $\lie$ an abstract quantum Lie algebra $\qlie$ independent of any concrete realization. Its h-dependent structure constants are given in terms of inverse quantum Clebsch-Gordan coefficients. We then show that all concrete quantum Lie algebras $\lqlie$ are isomorphic to an abstract quantum Lie algebra $\qlie$. In this way we prove two important properties of quantum Lie algebras: 1) all quantum Lie algebras $\lqlie$ associated to the same $\lie$ are isomorphic, 2) the quantum Lie product of any $\lqlie$ is q-antisymmetric. We also describe a construction of $\lqlie$ which establishes their existence.
Description: deformations
Delorm, M.
Extensions in the category O of Bernstein-Gelfand-Gelfand. Applications.
Funk. Anal. Pril. 14 (1980), N3, 77-78
Availability: hardcopy
Demazure, Michel
Classification des algebres de Lie filtrees
Se'min. Bourbaki 1966/67, No.326, 11 p. (1968)
Zentralblatt: 0209.06703
Availability: hardcopy
Demazure, M. and Gabriel, P.
Groupes algébrique, Tome I
Masson & Cie and North-Holland, 1970
Availability: Kolkhoz; Euler's library; absent on amazon
Demidov, E.E.
Kvantovye Gruppy
URL: http://www.krelib.com/matematika/559 http://techlibrary.ru/books.htm
Faktorial, Moscow, 1998 (in Russian); paperback, 127 pp.
Availability: hardcopy (book)
Demidov, S.S.
K istorii teorii S. Lie differencialnykh uravneniii s chastnymi proizvodnymi
Istoriko-Matematicheskie Issledovaniya XXIII (1978), 87-117
Availability: slie.djvu
Demmel, James W.
Applied Numerical Linear Algebra
URL: demmel/Demmel_J_W__Applied_Numerical_Linear_Algebra.djvu
Description: Including Lanczos method.
Availability: Kolkhoz' obmennik
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Dempster, A. P.
Covariance selection
DOI: 10.2307/2528966
Biometrics 28 (1972), No. 1 (Special Multivariate Issue), 157-175
Description: A multivariate normal model is proposed where inverse covariate matrix has zero at least at the same places as the covariate matrix itslef.
Availability: 1972-covariance.pdf
Demushkin, S.P.
Cartan subalgebras of the simple Lie p-algebras W_n and S_n
DOI: 10.1007/BF00967298
Sib. M.J. 11(1970), N2, 310-325
Description: Explicit determination of representatives in the conjugacy classes of Cartan subalgebras. In particular, every element in W_n\(W_n)_0 is conjugate to d/dx_1.
Availability: hardcopy
Denes, J. and Keedwell, A.D.
Latin Squares and Their Applications
Akademiai Kiado, Budapest, 1974
Zentralblatt: 0283.05014
Deng, S. and Hou, Z. and Kaneyuki, S. and Nishiyama, K.
Dipolarization in semisimple Lie algebras and homogeneous paraka"hler manifolds
J. Lie Theory 9 (1999), No. 1, 215-232
Description: Graded semisimple Lie algebras
Deodhar, Vinay V. and Gabber, Ofer and Kac, Victor
Structure of some categories of representations of infinite-dimensional lie algebras
DOI: 10.1016/S0001-8708(82)80014-5
Advances in Mathematics Volume 45, Issue 1, July 1982, Pages 92-116
Zentralblatt: 0491.17008
Description: Vanishing of some Ext^1 in the analogue of category O for Kac-Moody algebras. A simplified exposition is in Kac's book.
Availability: 1982-structure.pdf
Deonier, Richard C. and Tavare, Simon and Waterman, Michael S.
Computational genome analysis. An introduction
Springer, 2005. xx+534pp
Dergachev, Vladimir
Index of Lie algebras and associative algebras
Dissertation, Univ. Pennsylvania, 2000
Some properties of index of Lie algebras
arXiv:math/0001042
Description: Index of Lie algebars associated to a tensor product of associative algebras.
On associative algebras with unity and Lie index 1
arXiv:math/0005161
Description: Classification of 3-dim. associative algebras according to index.
On a new approach to classification of associative algebras
arXiv:math/0203013
A non radical based approach to study of associative algebras
arXiv:math.RA/0212369
Description: In the spirit of minimal polynomials.
Deriziotis
URL: http://osdir.com/ml/mathematics.gap.user/2007-12/msg00011.html
Description: All the rational subalgebras of simple Lie algebras gotten by Dynkin's classification can be found as centralisers of semisimple elements.
Deryabina, G. S.
On infinite p-groups with cyclic subgroups
DOI: 10.1070/SM1985v052n02ABEH002901
Mat. Sb. 124 (1984), N4, 495-504
Math. USSR Sbornik 52 (1985), 481-490
MR 754473
Zentralblatt: 0556.20032
Description: Development of theme if Olshanskii (continuum such groups, etc.)
Deryabina, G.S. and Olshanskii, A.Yu.
Subgroups of quasi-finite groups
DOI: 10.1070/RM1986v041n06ABEH004230
Rus. Math. Surv. 41 (1986), N6, 203-204
Description: An infinite groups is called quasi-finite, if all its proper subgroups are finite. It is studied, when a finite group may be embedded into quasi-finite group.
Availability: hardcopy
De'sarme'nien, Jacques and Duchamp, Ge'rard and Krob, Daniel and Melanc,on, Guy
Quelques remarques sur les super-alge`bres de Lie libres
C. R. Acad. Sci., Paris, Se'r. I 318, No.5, 419-424 (1994)
Zentralblatt: 0801.17004
Desoer, C.A.
Notes for a Second Course on Linear Systems
Van Nostrand Reinhold Co., 1970; paperback, 199 pp.
Availability: hardcopy (book)
Desrosiers, P. and Lapointe, L. and Mathieu, P.
Symmetric functions in superspace
math.CO/0412306
Deuring, M
Algebren
2nd ed., Springer, 1968
Availability: Kolkhoz
DeWitt, B.S.
Supermanifolds
College Press, Univ. of Beijing, 1998 (reprint of the 1984 edition); paperback, small format, 407 pp.
Availability: hardcopy (book)
Deza, Michel-Marie and Deza, Elena
Dictionary of Distances
Elsevier, 2006
Availability: 2006-dictionary.djvu
Di Battista, G. and Lenzerini, M.
Deductive entity relationship modeling
IEEE Trans. Knowledge and Data Engineering 1993 Volume: 5, Issue: 3 page(s): 439-450
Description: Not interesting for snark.
Availability: 00224196.pdf
Di Nasso, Mauro and Forti, Marco
Ultrafilter semirings and nonstandard submodels of the Stone-Cech compactification of the natural numbers
Preprint
Description: An attempt to introduce reasonable algebraic operations on the set of ultrafilters.
Availability: 18.pdf
Di Vincenzo, Onofrio Mario
Polynomial identities for graded algebras
Polynomial Identities and Combinatorial Methods (ed. A.Giambruno, A.Regev, M.Zaicev), LN Pure Appl. Math. 235, M.Dekker, 2003, 203-
Description: Associative algebras and superalgebras.
Availability: di.tar (first few pages only)
google books
Di Vincenzo, O.M. and Drensky, V. and Nardozza, V.
Subvarieties of the variety generated by the 2 x 2 matrix superalgebra
C. R. Acad. Bulgare Sci. 54 (2001), no. 12, 9--12
Diaconescu, Razvan
Institution-independent Model Theory
DOI: 10.1007/978-3-7643-8708-2
Description: Los theorem about ultraproducts in seemingly very general setting.
Availability: 2008-chapter6. pdf (Chapter 6 only)
Diaconis, P.
Group Representations in Probability and Statistics
Inst. Math. Stat., 1988
MR 964069
Availability: Kolkhoz; absent on amazon
Dias da Silva, J.A. and Rodrigues, Fa'tima
Decomposable critical tensors
Linear Algebra and its Applications Volume 414, Issue 1 , 1 April 2006, Pages 172-198
Description: Young symmetrizers, decomposable elements.
Availability: sdarticle.pdf
Diaz, Rafael and Pariguan, Eddy
Graphical introduction to classical Lie algebras
math.RT/0504602
Dicks, Warren
On the cohomology of one-relator associative algebras
J. Algebra 97 (1985), 79-100
MR 87h:16041
A survey of recent work on the cohomology of one-relator associative algebras.
Ring theory (Granada, 1986), Lecture Notes in Math. 1328 (1988), 75-81
MR 89m:16049
Dickson, L.E.
Differential equations from the group standpoint
Annals of Math. Vol. 25, 287-378
Availability: diffeq.djvu
History of the Theory of Numbers, Vol. I, II, III
Chelsea Publ. Co., 1952, 1971, 1992 (reprint of Carnegie Inst. of Washington, 1919, 1920, 1923)
Availability: Kolkhoz
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Algebras and Their Arithmetics
G.E. Stechert & Co., New York, 1938 (reprint of the 1923 edition); hardcover, small format, 241 pp.
Availability: hardcopy (book); amazon
New First Course in the Theory of Equations
Wiley, 1955 (10th printing of the 1939 edition); hardcover, 185 pp.
Availability: hardcopy (book)
Linear Groups with an Exposition of the Galois Field Theory
URL: http://mathbooks.library.cornell.edu:8085/Dienst/UIMATH/1.0/Display/cul.math/05110001 http://da8.boom.ru/ct/algebra.htm
Availability: Kolkhoz
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Dieterich, Ernst
Dissident algebras
Colloq. Math 82 (1999), N1-2, 13-23
Description: Some algebras defined starting from V \wedge V -> V linear map; related with 1-2-4-8-division-algs theme.
Eight-dimensional real quadratic division algebras
Annonces de Montpellier en Algèbre, 01-2000
Availability: EMIS site
Real quadratic division algebras
Comm. Alg. 28 (2000), N2
Quadratic division algebras revisited (Remarks on an article by J. M. Osborn)
Proc. Amer. Math. Soc. 128 (2000), 3159-3166.
Abstract: In his remarkable article ``Quadratic division algebras'' (Trans. Amer. Math. Soc. 105 (1962), 202-221), J. M. Osborn claims to solve `the problem of determining all quadratic division algebras of order 4 over an arbitrary field of characteristic not two modulo the theory of quadratic forms over ' (cf. p. 206). While we shall explain in which respect he has not achieved this goal, we shall on the other hand complete Osborn's basic results (by a reasoning which is finer than his) to derive in the real ground field case a classification of all 4-dimensional quadratic division algebras and the construction of a 49-parameter family of pairwise nonisomorphic 8-dimensional quadratic division algebras. To make these points clear, we begin by reformulating Osborn's fundamental observations on quadratic algebras in categorical terms.
Classification, automorphism groups and categorical structure of the two-dimensional real division algebras.
DOI: 10.1142/S0219498805001307
J. Algebra Appl. 4 (2005), no. 5, 517--538
Dieudonné, Jean
Mémoire de Bertram Kostant sur les applications de la cohomologie des algèbres de Lie réductives
Séminaire Bourbaki 8 (1962-1964), Exposé No. 243, 13 p.
MR 1611529
Zentralblatt: 0134.26702
Description: Exposition of the famous Kostant's paper where he proves the Amitsur-Levitski theorem by cohomological methods.
La geometrie des groupes classiques
URL: http://techlibrary.ru/books.htm http://orel721.rsl.ru/books_09.06/1/735.djvu
Mir, 1974 (translation from the 3rd ed., Springer, 1971)
Availability: Kolkhoz (Russian edition); 1971-geometrie.djvu
Dieudonné, J. and Carrel, J.B. and Mumford, D.
Invariant Theory, Old and New and Geometric Invariant Theory
Merkurii-Press, 2000 (Russian translation from Dieudonné and Carrel's Adv. Math. 1970 paper (revised as a small book - Academic Press, 1971) and part of Mumford's 1965 book) paperback, small format, 280 pp
Zentralblatt: 0258.14011
Availability: absent on amazon; hardcopy (book); hardcopy (Adv. Math. paper, photocopy); Kolkhoz
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Digne, F. and Michel, J.
Representations of Finite Groups of Lie Type
Cambridge Univ. Press, 1991; paperback, 159 pp.
Availability: hardcopy (book)
Dijkstra, t. K.
Some properties of estimated scale invariant covariance structures
DOI: 10.1007/BF02295290
Psychometrika Volume 55, Number 2 / June, 1990 Pages 327-336
Description: Estimation of covariance matrix dependent on parameters.
Availability: 1990-some.pdf
Dimitric, Radoslav M.
Algebraic compactness of $\prod M_\alpha/\bigoplus M_\alpha$
Int. J. Pure Appl. Math. 14, No.1, 61-66 (2004)
Zbl: pre02104196
Availability: ALGCOJPA.pdf
Dirac, P.A.M.
Generalized hamiltonian dynamics
Canad. J. Math. 2 (1950), No.2, 129--148.
Description: Poisson brackets
Availability: hardcopy (book)
Generalized hamiltonian dynamics
Proceedings of the Royal Society A 246 (1958), 326--332
Description: Poisson brackets
Availability: hardcopy (book)
Lekcii po teoreticheskoi fizike
Regular & Chaotic Dynamics, 2001 (Russian translation from Lectures on Quantum Mechanics, Yeshiva Univ., 1964 and General Theory of Relativity); paperback, 240 pp.
Description: Dirac brackets - a special amazing type of agreed Poisson brackets. Contains also two preceding Dirac papers on the subject.
Availability: hardcopy (book); Kolkhoz
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Dito, Giuseppe and Sternheimer, Daniel
Deformation Quantization: Genesis, Developments and Metamorphoses
math.QA/0201168
Proceedings of the meeting between mathematicians and theoretical physicists, Strasbourg, 2001. IRMA Lectures in Math. Theoret. Phys., vol. 1, Walter De Gruyter, Berlin 2002, pp. 9--54
Abstract: a survey
Dixmier, J.
Sur les algebres derivees d'une algebre de Lie
Proc. Camb. Philos. Soc. 51 (1955), 541-544
Zentralblatt: 0066.02402
Description: Lower estimates on dim L^i/L^(i+1) for a nilpotent L.
Cohomologie des algebres de Lie nilpotentes
Acta Sci. Math. Szeged 16 (1955), 246-250
Zentralblatt: 0066.02403
Description: Some exact sequence in Lie alg. (co)homology with trivial coeff.; some estimates on dim H^i(L,K) for L nilpotent.
Availability: hardcopy; dixmier-bmp.tar.bz2 (huge scans of a very low quality)
Enveloping Algebras
URL: http://techlibrary.ru/books.htm http://orel721.rsl.ru/books_09.06/1/710.djvu
AMS, The 1996 printing of the 1997 English translation; hardcover
Availability: hardcopy (book); Kolkhoz (Russian edition); amazon
Dixmier, J. and Lister, W.
Derivations of nilpotent Lie algebras
PAMS 8(1957), 155-158
Description: An example of 8-dimensional nilpotent Lie algebra all whose derivations are nilpotent. Introduced a notion of characteristically nilpotent Lie algebra.
Availability: dixmier.pdf
Dixon, J. D. and Du Sautoy, M. P. F. and Mann, A. and Segal, D.
Analytic Pro-P Groups
Description: Multiple interplay with Lie algebras.
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Dixon, Martyn R. and Evans, Martin J. and Smith, Howard
A Tits alternative for groups that are residually of bounded rank
Israel J. Math. 109 (1999), 53-59
MR 2000d:20036
Zentralblatt: 0924.20023
Dixon, H. and Ginsberg, M. and Hofer, D. and Luks, E. and Parkes, A.
Generalizing boolean satisfiability III: Implementaion
Journal of Artificial Intelligence Research, 23, (2005), 441-531
Dixon, H. and Ginsberg, M. and Luks, E. and Parkes, A.
Generalizing boolean satisfiability II: Theory
Journal of Artificial Intelligence Research, 22, (2004), 481-534
Dixon, Geoffrey
Division algebras: Octonions, Quaternions, Complex Numbers, and the Algebraic Design of Physics
Kluwer, 1994
Dixon, J.D.
Problems in Group Theory
Dover, 1973 (republication of Blaisdell Publ. Co., 1967); paperback, 176 pp.
Availability: hardcopy (book); Kolkhoz
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Review of "Infinite linear groups" by B.A.F. Wehrfritz
BAMS 80 (1974), N6, 1071-1074
Availability: hardcopy
The Tits alternative
Preprint, 1988
Description: An little bit alternative simplified proof.
Availability: TITSALT.pdf; hardcopy
Djokovic, Dragomir Z.
Real homogeneous algebras
DOI: 10.2307/2039113
Proc. AMS 41 (1973), No.2, 457-462
Zentralblatt: 0251.16017
Description: Algebra is called homogeneous, if its automorphism group acts transitively on one-dimensional subspaces.
Availability: output.pdf
An elementary proof of the Baker-Campbell-Hausdorff-Dynkin formula
Math. Z. 143 (1975), N3, 209-211
Availability: PPN266833020_0143__0_0.pdf
Classification of some 2-graded Lie algebras
DOI: 10.1016/0022-4049(76)90033-5
J. Pure Appl. Alg. 7 (1976), N2, 217-230
MR 52:10822
Zentralblatt: 0319.17005
Classification of Z-graded real semisimple Lie algebras
J. Alg. 76 (1982), 367-382
Description: Also description of gradings in complex Lie algebras in terms of weighted Dynkin diagrams.
Availability: hardcopy
On some inner derivations of free Lie algebras over commutative rings
J. Alg. 119 (1988), 233-245
Description: Decomposition of free Lie alg L = Ka + Ker(ad a)
Availability: hardcopy
Automorphisms of the Lie algebra of upper triangular matrices over a connected commutative ring
DOI: 10.1006/jabr.1994.1329
J. Algebra 170 (1994), No.1, 101-110
Availability: science-1.pdf
Djokovic, D. and Patera, J. and Winternitz, P. and Zassenhaus, H.
Normal forms of elements of classical real and complex Lie and Jordan algebras
DOI: 10.1063/1.525868
J. Math. Phys. 24(1983), N6, 1363-1374
Description: Equivalence classes under corresponding Lie group action.
Availability: JMathPhys_24_1363.pdf
Djokovic, Dragomir Z. and Smith, Benjamin H.
Quaternionic matrices: Unitary similarity, simultaneous triangularization and some trace identities
arXiv:0709.0513
To appear in Linear Algebra and Its Applications
Djokovic, Dragomir Z. and Sweet, Lowell G.
Infinite homogeneous algebras are anticommutative
URL: https://www.ams.org/proc/1999-127-11/S0002-9939-99-04910-2/S0002-9939-99-04910-2.pdf http://links.jstor.org/sici?sici=0002-9939(199911)127%3A11%3C3169%3AIHAAA%3E2.0.CO%3B2-K
Proc. Amer. Math. Soc. 127 (1999), 3169-3174
Description: A (non-associative) algebra is called homogeneous if its automorphism group permutes transitively the one dimensional subspaces.
Djokovic, Dragomir Z. and Zhao, Kaming (=Zhao, Kai Ming, =Zhao, Kaiming)
Derivations, isomorphisms, and second cohomology of generalized Block algebras
Algebra Colloquium 3 (1996)
Generalized Cartan type W Lie algebras in characteristic zero
DOI: 10.1006/jabr.1997.7067
J. Algebra 195 (1997), No.1, 170-210
Description: Lie algebras of the form L\otimes A, L acts on A as derivations, {x\otimes a, y\otimes b} = x\otimes b(y(a)) - y\otimes a(x(b)) + [x,y]\otimes ab (like in Jordan et al.) Automorphisms, derivations, subalgebras, H^2(L,K).
Availability: science.pdf
Derivations, isomorphisms, and second cohomology of generalized Witt algebras
URL: http://www.ams.org/tran/1998-350-02/S0002-9947-98-01786-3/home.html http://links.jstor.org/sici?sici=0002-9947(199802)350%3A2%3C643%3ADIASCO%3E2.0.CO%3B2-3
Trans. Amer. Math. Soc. 350 (1998), 643-664
Invariant theory for non-associative real two-dimensional algebras and its applications
DOI: 10.1007/s00031-004-7001-7
Transformation Groups 9 (2004), N1, 3-23
Description: (A usual) space-of-structure-constants-and-action-of-GL(n) business.
Real homogeneous algebras as truncated division algebras and their automorphism groups
Algebra Colloq. 11 (2004), no.1, 11-20
Description: Truncation is an opertion of obtaining a new alebra structure defined on a subspace of a given algebra by projection. Truncations of quaternions and octonions.
Availability: 14175318.pdf
Real division algebras with large automorphism group
DOI: 10.1016/j.jalgebra.2004.03.015
J. Algebra 282 (2004), N2, 758-796
DLAB, VLASTIMIL and RINGEL, CLAUS MICHAEL
EVERY SEMIPRIMARY RING IS THE ENDOMORPHISM RING OF A PROJECTIVE MODULE OVER A QUASI-HEREDITARY RING
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 107. Number I . September 1989, 1-5
Availability: 1989-every.pdf
Dobrev, V.K.
Representations and characters of the Virasoro algebra and N=1 super-Virasoro algebras
arXiv:0709.0105
Description: An article from some (math physics?) encyclopedia.
Dobrovolska, Galyna and Kim, John and Ma, Xiaoguang
On the lower central series of an associative algebra
DOI: 10.1016/j.jalgebra.2008.02.019
arXiv:0709.1905
J. Algebra 320 (2008), N1, 213-237
Description: General results about lower central series of a Lie algebra associated with an associative algebra.
Dobrynin, N. A.
Free partially commutative Lie superalgebras: dimensions of homogeneous components
J. Math. Sci. 102(2000), 4566-4580
Description: A VINITI survey. Color algebras.
Doherty, Faun C.C.
A history of finite simple groups
M.Sc. Thesis, U. Colorado, 1997
Availability: fdoherty.ps
Dokas, Ioannis
Quillen-Barr-Beck (co-) homology for restricted Lie algebras
J. Pure Appl. Algebra 186(2004), no. 1, 33--42
Abstract: In this paper we use Quillen-Barr-Beck's theory of (co-) homology of algebras in order to define (co-) homology for the category RLie of restricted Lie algebras over a field k of characteristic p0. In contrast with the cases of groups, associative algebras and Lie algebras we do not obtain Hochschild (co-) homology shifted by 1. Precisely, we determine for LRLie the category of Beck L-modules and the group of Beck derivations of gRLie/L to a Beck L-module M. Moreover, we prove a classification theorem which gives a one-to-one correspondence between the one cohomology and the set of equivalent classes of p-extensions. Finally, a universal coefficient theorem is proved, relating the homology to the Hochschild homology via a short exact sequence. This shows that the new homology determines the Hochschild homology.
Availability: science.pdf
Dokas, Ioannis and Loday, Jean-Louis
On restricted Leibniz algebras
DOI: 10.1080/00927870600938803
arXic:math.RA/0506473
Comm. Algebra 34 (2006), N12, 4467-4478
Description: Structures on the tensor product of Leibniz and Zienbel algebras.
Dolan, Louise
The Beacon of Kac-Moody Symmetry for Physics
Notices of the AMS, December 1995
Dold-Samplonius, Yvonne
Interview with Bartel Leendert van der Waerden
Notices AMS, March 1997
Dolfi, Silvio and Herzog, Marcel and Kaplan, Gil and Lev, Arieh
The size of the solvable residual in finite groups
Groups Geom. Dyn. 1 (2007), no. 4, 401--407
Zentralblatt: pre05233105
Description: For any finite group G with a trivial Frattini subgroup, the size of the smallest normal subgroup such that quotient is solvable, is > |G|^b, where b = 0.700...
Dolgachev, I.V.
The Euler characteristic of a family of algebraic varieties
Sbornik Mathematics 18 (1972), Number 2, 303-319
Availability: Dolgachev.pdf
Dolguntseva, I.A.
The Hochschild cohomology for associative conformal algebras
Algebra Logic 46 (2007), no. 6, 373--384
MRMR 2389419 (me)
Availability: hardcopy
Dolgushev, Vasiliy
A proof of Tsygan's formality conjecture for an arbitrary smooth manifold
math.QA/0504420
PhD Thesis, MIT
A formality theorem for Hochschild chains
Adv. Math. 200(2006), N1, 51-101
(me)
Availability: hardcopy
Formality theorem for Hochschild (co)chains of the algebra of endomorphisms of a vector bundle
math.KT/0608112
Erratum to: "A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold"
math.QA/0703113
Dolinka, Igor and Mudrinski, Nebojsa
On subdirect decomposition and varieties of some rings with involution. II
Novi Sad J. Math. 34 (2004), no. 2, 109--117
Domokos, Matyas
Cayley-Hamilton theorem for 2x2 matrices over the Grassman algebra
Preprint
Availability: CH.{tex,dvi}
Donadze, Guram and Inassaridze, Nick and Porter, Timothy
N-Fold Cech Derived Functors and Generalised Hopf type formulas
math.KT/0303050, 30 pages
K-Theory Preprints Archive, N624
Hopf Topology Archive, March 2003
Abstract: In 1988, Brown and Ellis published a generalised Hopf formula for the higher homology of a group. Although substantially correct, their result lacks one necessary condition. We give here a counterexample to the result without that condition. The main aim of this paper is, however, to generalise this corrected result to derive formulae of Hopf type for the n-fold Cech derived functors of the lower central series functors Z_k. The paper ends with an application to algebraic K-theory.
Donald, J.D. and Flanigan, F.J.
A deformation theoretic version of Maschke's theorem for modular group algebras: the commutative case
DOI: 10.1016/0021-8693(74)90114-8
J. Alg. 29 (1974), 98-102
Zentralblatt: 0275.20008
Availability: 1974-maschke.pdf; hardcopy
Deformations of algebra modules
DOI: 10.1016/0021-8693(74)90066-0
J. Alg. 31 (1974), 245-256
Zentralblatt: 0283.16016
Availability: 1974-deformations.pdf
Donaldson, S. K.
Lie algebra theory without algebra
arXiv:math.DG/0702016
Algebra, Arithmetic and Geometry. Volume I: In Honor of Y.I. Manin, Progress in Mathematics , Vol. 269 Tschinkel, Yuri; Zarhin, Yuri G. (Eds.), Springer, 2008
Abstract: This is an expository paper in which we explain how basic, standard, results about simple Lie algebras can be obtained by geometric arguments, following ideas of Cartan, Richardson and others.
Dong, C. and Griess, R. L. Jr
Automorphism groups and derivation algebras of finitely generated vertex operator algebras
Michigan Math. J. Volume 50 , Issue 2 August 2002, 227-239
math.QA/0106051
Dong, Liu and Lei, Lin
On the variations of G_2
Chin. Ann. Math. 24B (2003), N3, 387-294
Description: Simple Lie algebras over p=2.
Availability: mathpaper16.pdf
Dong, Ch. and Lepowsky, J.
Generalized Vertex Algebras and Relative Vertex Operators
Progress in Mathematics, Vol. 112, Birkhauser, 1993
Availability: $72
Dong, Ch. and Li, Haisheng and Mason, G.
Vertex Lie algebras, vertex Poisson algebras and vertex algebras
in: Contemp. Math. 297(2002)
Dong, Chongying and Mason, Geoffrey
Local and Semilocal Vertex Operator Algebras
math.QA/0409410
J. Alg. 280 (2004), 350-366
Description: General structure theory for a vertex operator algebras, in the spirit of the ring theory.
Donin, Joseph
On the quantization of Poisson brackets
q-alg/9505028
Int. J. Mod. Phys. A 11 (1996), 863-886
Availability: hardcopy
Donin, Dmitry and Khesin, Boris
Pseudodifferential symbols on Riemann surfaces and Krichever-Novikov algebras
DOI: 10.1007/s00220-007-0234-2
Comm. Math. Phys. 272 (2007), no. 2, 507--527
Description: Including derivations and central extensions.
Donin, Joseph and Mudrov, A.
Method of quantum characters in equivariant quantization
Preprint, April 22, 2002, 28pp.
Availability: hardcopy
Reflection equation, twist, and equivariant quantization
Preprint, April 23, 2002, 17pp.
Availability: hardcopy
Donin, Joseph and Shnider, Steven
Cohomological construction of quantized universal enveloping algebras
Trans. Amer. Math. Soc. 349 (1997), 1611-1632
arXiv:q-alg/9506013
Donkin, Stephen and Erdmann, Karin
Tilting Modules, Symmetric Functions, and the Module Structure of the Free Lie Algebra
Journal of Algebra Vol. 203, No. 1, May 1, 1998 pp. 69-90
Dorai, P. and Rema, P.S.
Prime ideals in a Lie algebra
DOI: 10.1016/0021-8693(80)90099-X
J. Algebra 66 (1980), N2, 492-504
Availability: 1980-prime.pdf
Doran, Charles F. and Faux, Michael G. and Gates, S. James Jr. and Hubsch, Tristan and Iga, Kevin M. and Landweber, Gregory D.
Off-shell supersymmetry and filtered Clifford supermodules
math-ph/0603012, 22 p.
Description: Gerstenhaber theory that filtered algebras is a deformation of associated graded algebra extended to superalgebras and deformations of modules, and to bifiltrations and bigradings.
Doran-Wu, Patrick
Extension of Lie's algorithm: a potential symmetries classification of PDEs
PhD Thesis, 1996
Dorfmeister, Josef
Varietes homogenes kahleriennes
CRAS 301 (1985), 97-98
Description: Kahler Lie algebras: j:L->L with [jx,jy] = j[jx,y] + j[x,jy] + [x,y], etc.
Availability: hardcopy
Algebraic systems in differential geometry
Jordan Algebras, deGruyter, 1994, 9-33
Availability: hardcopy
Dorfmeister, Josef and Nakajima, Kazufumi
La conjecture fondamentale pour les varietes homogenes kahleriennes
CRAS 303(1986), N8, 335-338
Description: A notion of Kahler Lie algebra as a Lie algebra g with subalgebra h, skew symmetric bilinear form and j:g->g with axioms like [jx,jy] = j[jx,y] + j[x,jy] + [x,y] mod h.
Availability: hardcopy
Dorodnitsyn, V.A.
Finite difference models entirely inheriting continuous symmetry of original differential equations
Int. J. Mod. Phys. C 5 (1994), 723--734
Gruppovye svoistva raznostnykh uravnenii
Fizmatlit, Moscow, 2001 (in Russian)
Availability: Kolkhoz
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Dorodnitsyn, V. and Kozlov, R. and Winternitz, P.
Symmetries, Lagrangian Formalism and Integration of Second Order Ordinary Difference Equations
Journal of Nonlinear Mathematical Physics Volume 10, Supplement 2, December 2003 , 41-56
Dosiev, Anar A.
Algebras of power series of elements of a Lie algebra, and Slodkowski spectra
DOI: 10.1023/B:JOTH.0000042449.24890.cf
Zapiski Nauchn. Semin. POMI 290 (2002), 72-121
Journal of Mathematical Sciences Volume 124, Number 2 / November, 2004 Pages 4886-4908
Description: Proposition 1.2 and Lemma 1.7 - something like behaviour of (co)homology under ultraproduct construction (in some Banach spaces setting).
Availability: hardcopy
Dotsenko, Vladimir V.
Homology of the Lie algebra of vector fields on the line with coefficients in symmetric powers of its adjoint representation
Funct. Anal. Appl. 40 (2006), N2, 91-96
Description: Homology of W_1 \otimes C[t] up to degree 5.
Availability: 9456826p7030p460.pdf
An operadic approach to deformation quantization of compatible Poisson brackets
J. Gen. Lie Theory and Appl. 1 (2007), No. 2, 107-115
arXiv:math.QA/0611154
Compatible associative products and trees
arXiv:0809.1773
Description: Free objects in the category of two compatible associative structures. The languge and technique are operadic.
Dotsenko, Vladimir and Khoroshkin, Anton
Character formulas for the operad of two compatible brackets and for the bihamiltonian operad
DOI: 10.1007/s10688-007-0001-3
arXiv:math.QA/0605233
Funct. Anal. Prilozh. 41 (2007), N1, 1-17
Description: Operadic approach to compatible Lie brackets.
Doty, Stephen and Henke, Anne
Decomposition of tensor products of modular irreducibles for SL_2
The Quarterly Journal of Mathematics 2005 56(2):189-207
Doubrov, Boris M. (=Dubrov) and Komrakov, Boris P.
Contact Lie algebras of vector fields on the plane
math.DG/9903198
Geom. Topol. 3 (1999), 1-20
Zentralblatt: 0955.17016
Description: Classification of all real Lie algebras of contact vector fields on the first jet space of one-dimensional submanifolds in the plane. This completes Sophus Lie's classification of all possible Lie algebras of contact symmetries for ordinary differential equations. As a main tool one used the abstract theory of filtered and graded Lie algebras. This may be described as deformation-theoretic problem, though deformation theory is not used here.
The problem of constructive equivalence in differential geometry
URL: http://www.turpion.org/php/paper.phtml?journal_id=sm&paper_id=476 URL http://math.ras.ru/Mat._sbornik/Soderzhanie/?biblio=yes&page=39&abstract=rus&address=sABJB.AFwfyil5h
Sbornik Mathematics 191 (2000), Number 5, 655-681
Description: Lie symmetries and differential equations. Question of eqivalence of transitive Lie algebas of vector fields (with fixed subalgebras g_0).
Availability: equiv-matsb.pdf
Doubrov, Boris and Komrakov, Boris and Morimoto, Tohru
Equivalence of holonomic differential equations
Lobachevskii J. Math. 3(1999), 39-71
Description: "Modern" theory of differential equations (jet spaces etc.), prolongation of Lie algebras, Lie algebars of vector fields, and all that. Concrete examples at the end.
Dourlens, Sophie
On the Hochschild cohomology of triangular algebras
DOI: 10.1081/AGB-120023137
Comm. Algebra 31 (2003), N10, 4871-4897
Abstract: In order to study the Hochschild cohomology of an n-triangular algebra n, we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with n, and which converges to the Hochschild cohomology of n. We describe explicitly its components and its differentials which are sums of cup products. In case n = 3 we study some properties of the differential at level 2. We give some examples of use of the spectral sequence and recover formulas for the dimension of the cohomology groups of particular cases of triangular algebras.
Dowbor, Piotr and Hajduk, Adam
A comparison of various types of degenerations for algebras
Algebra Colloquium 14 (2007), No.3, 361-388
Dowd, Michael F. and Sin, Peter
On representations of algebraic groups in characteristic two
Preprint
Description: Also for Lie (classical) algebras; particularly, all extensions between simple modules for Lie algebras of rank <= 4 are computed.
Availability: chartwo.ps
Downes, J. and Goodman, J.E.
Dictionary of Finance and Investment Terms
5th ed., Barron's Educational Series, 1998; softcover, small format, 730 pp.
Availability: hardcopy (book)
Doyon, Benjamin and Lepowsky, James and Milas, Antun
Twisted vertex operators and Bernoulli polynomials
math.QA/0311151
Abstract: Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an arbitrary twisting automorphism. The construction involves the Bernoulli polynomials in a fundamental way. We develop new identities and principles in the theory of vertex operator algebras and their twisted modules, and explain the construction by applying general results, including an identity that we call modified weak associativity, to the Heisenberg vertex operator algebra. This paper gives proofs and further explanations of results announced earlier. It is a generalization to twisted vertex operators of work announced by J. L. some time ago, and includes as a special case the proof of the main results of that work.
Dragovich, Branko and Dragovich, Alexandra
A p-adic model of DNA-sequence and genetic code
arXiv:q-bio/0607018
p-adic modelling of the genome and the genetic code
arXiv:0707.3043
Draisma, Jan
Lie algebras of vector fields
PhD Thesis, TU Eindhoven, 2002
Availability: thesis.pdf
On a conjecture of Sophus Lie
Diff. equations and the Stockes phenomenon (ed. B.L.J.Braaksma et al.), World Sci., 2002, 65-87
Zentralblatt: (me)
Availability: hardcopy
Constructing Lie algebras of first order differential operators
J. Symbolic Computation 36(2003), N5, 685-698
Abstract: We extend Guillemin and Sternberg's Realization Theorem for transitive Lie algebras of formal vector fields to certain Lie algebras of formal first order differential operators, and show that Blattner's proof of the Realization Theorem allows for a computer implementation that automatically reproduces many realizations derived in the existing literature, and that can also be used to compute new realizations. Applications include the explicit construction of quasi-exactly solvable Hamiltonians, and of finite-dimensional irreducible modules over semisimple Lie algebras.
Availability: difop.pdf
Draisma, Jan and Kraft, Hanspeter and Kuttler, Jochen
Nilpotent subspaces of maximal dimension in semi-simple Lie algebras
Compositio Mathematica 142 (2006), 464-476
Abstract: We show that a linear subspace of a reductive Lie algebra $\operatorname{\mathfrak g}$ that consists of nilpotent elements has dimension at most $\frac{1}{2}(\dim\operatorname{\mathfrak g}-\operatorname{rk}\operatorname{\mathfrak g})$, and that any nilpotent subspace attaining this upper bound is equal to the nilradical of a Borel subalgebra of $\operatorname{\mathfrak g}$. This generalizes a classical theorem of Gerstenhaber, which states this fact for the algebra of $(n\times n)$-matrices.
Drápal, A. and Jezek, J. and Kepka, T.
Groupoids and the associative law. IX: Associative triples in some classes of groupoids
Acta Univ. Carol., Math. Phys. 38, No.1, 39-52 (1997)
Zentralblatt: 0889.20042
Description: ... the maximal and minimal numbers of associative triples in the following classes of groupoids: All groupoids, commutative groupoids, commutative distributive groupoids and quasitrivial groupoids.
Draper, Cristina
Models of the Lie algebra F4
DOI: 10.1016/j.laa.2008.01.009
Lin. Alg. Appl. 428 (2008), N11-12, 2813-2839
Abstract: We describe the models of the exceptional Lie algebra F4 which are based on its semisimple subalgebras of rank 4. The underlying fact is that any reductive subalgebra of maximal rank of a simple Lie algebra induces a grading on this algebra by means of an abelian group, in such a way that the nontrivial components of the grading are irreducible modules.
Draper, Cristina and Fernández López, Antonio and García, Esther and Gómez Lozano, Miguel
The socle of a nondegenerate Lie algebra
DOI: 10.1016/j.jalgebra.2007.10.042
Journal of Algebra Volume 319, Issue 6, 15 March 2008, Pages 2372-2394
Description: Nondegenarate means not having absolute zero divisors.
Draper, Cristina and Mart\'in, C\'andido
Gradings on the Albert Algebra and on $f_4$
math.RA/0703840
Draper, Cristina and Martin Gonzalez, Candido
Gradings on g_2
Linear Algebra Appl. 418 (2006), no. 1, 85--111; Erratum: 420 (2007), no. 2-3, 728
Draper, Cristina and Mart\'in, C\'andido and Viruel, Antonio
Fine Gradings on the exceptional Lie algebra $\mathfrak d_4$
arXiv:0804.1763
Draper, Cristina and Viruel, Antonio
Group gradings on ${\rm o}(8,\Bbb C)$
Rep. Math. Phys. 61 (2008), no. 2, 265--280
Draxl, P.K
Skew fields
URL: http://www.ams.org/bull/1984-11-01/S0273-0979-1984-15277-7/S0273-0979-1984-15277-7.pdf http://projecteuclid.org/euclid.bams/1183551852
Drazin, Michael P.
Generalizations of Fitting's lemma in arbitrary associative rings
Comm. Alg. 29 (2001), N8, 3647-3675
Availability: 100105047.pdf
Drensky (=Drenski), Vesselin S.
A minimal basis for identities of a second-order matrix algebra over a field of characteristic 0
Algebra i Logika 20 (1981), no. 3, 282290
Representations of the symmetric group and varieties of linear algebras
DOI: 10.1070/SM1982v043n01ABEH002411
Math. USSR Sbornik 43 (1982), N1, 85-101
MR 618589
Zentralblatt: 0465.17007
Description: Section 4: Var(sl(2)) is considered.
Availability: hardcopy
Codimensions of T-ideals and Hilbert series of relatively free algebras
J. Alg. 91 (1984), 1-17
Zentralblatt: 552.16006
Description: Structure (particularly, dimensions of homogeneous components) of relatively free algebra in Var(sl(2)).
Availability: science-3.pdf
T-ideals containing all matrix polynomial identities
DOI: 10.1080/00927878508823264
Communications in Algebra, Volume 13, Issue 9 1985 , pages 2037 - 2072
Description: Class of nilpotence of radical of relatively free algebras in Var(sl(2)).
Free Algebras and PI-Algebras
Springer, 2000; paperback, 271 pp.
Availability: hardcopy (book)
Drensky, V. and Formanek, E.
Polynomial Idenitity Rings
Birkhäuser, 2004, 200 pp.
Availability: 20EUR (sale); google books
Drensky, Vesselin and Gerritzen, Lothar
Nonassociative exponential and logarithm
DOI: 10.1016/j.jalgebra.2003.09.037
J. Algebra 272 (2004), no. 1, 311--320
Drensky, Vesselin (=Drenski) and Holtkamp, Ralf
Constants of formal derivatives of non-associative algebras, Taylor expansions and applications
arXiv:math.RA/0312082
Rend. Circ. Mat. Palermo 55 (2006), no. 3, 369--384
Abstract: We study unitary multigraded non-associative algebras R generated by an ordered set X over a field K of characteristic 0 such that the mappings d_k: x_l->delta_{kl}, x_k,x_l in X, can be extended to derivations of R. The class of these algebras is quite large and includes free associative and Jordan algebras, absolutely free (non-associative) algebras, relatively free algebras in varieties of algebras, universal enveloping algebras of multigraded Lie algebras, etc. There are Taylor-like formulas for R: Each element of R can be uniquely presented as a sum of elements of the form (...(r_0 x_{j_1})...x_{j_{n-1}}) x_{j_n}, where r_0 is a constant and j_1 <= ...<= j_n. We present methods for the description of the algebra of constants, including an approach via representation theory of the general linear or symmetric groups. As an application of the Taylor expansion for non-associative algebras, we consider the solutions of ordinary linear differential equations with constant coefficients from the base field.
Drensky (=Drenski), Vesselin and Piacentini Cattaneo, Giulia Maria
Varieties of metabelian Leibniz algebras
J. Algebra and its Applications 1 (2002), N1, 31-50
Zentralblatt: 1025.17001
Drensky, V.S. (=Drenski) and Racine, M.L.
Distinguishing simple Jordan algebras by means of polynomial identities
DOI: 10.1080/00927879208824343
Commun. Algebra 20, No.2, 309-327 (1992)
Zentralblatt: 0745.17027
Availability: 780128712.pdf
Dresner, L.
Applications of Lie's Theory of Ordinary and Partial Differential Equations
IOP Publ., 1999
Availability: Kolkhoz
Dries, L. van den and Wilkie, A. J.
Gromov's theorem on groups of polynomial growth and elementary logic
Journal of Algebra Volume 89, Issue 2 , August 1984, Pages 349-374
Description: Nonstandard analysis is utilized.
Availability: sdarticle-4.pdf
Driss, Aiat Hadj Ahmed and L'Moufadal, Ben Yakoub
A note on Lie derivations of upper triangular matrices over rings
JP Journal of Algebra, Number Theory and Applications, 4(2) (2004), 577-591
Drnovsek, R. and Radjavi, H. and Rosenthal, P.
A characterization of commutators of idempotents
Lin. Alg. Appl. 347(2002), 91-99
Description: In a ring, with excurses into operator theory.
Drollinger, Fritz
Ueber die Struktur nilpotenter und auflosbarer Liescher Algebren
Comm. Math. Helv. 42 (1967), 259-284
Droste, Manfred and Giraudet, Michele and Gobel, Rudiger
All groups are outer automorphism groups of simple groups
JLMS 64(2001), N3, 565-575
MR 2002h:20050
Availability: S0024610701002484a.pdf
Droste, Manfred and Shelah, Saharon
Outer Automorphism Groups of Ordered Permutation Groups
math.GR/0010304
Description: Every group is isomorphic to the outer automorphism group of the automorphism group of some doubly homogeneous chain.
Drozd, Yuriy A.
On the representations of the Lie algebra sl_2 (Ukrainian)
Visn. Kiiv. Univ. Mat. i Mekh. 25 (1983), 70-77
Availability: hardcopy
Derived tame and derived wild algebras
arXiv:math.RT/0310171
Abstract: We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.
Drozd, Yu.A. and Kirichenko, V.V.
Finite Dimensional Algebras
Kiev, 1980 (in Russian)
Availability: amazon; 1980-finite-dim.djvu; Kolkhoz
Drton, Mathias
Algebraic techniques for Gaussian models
arXiv:math.ST/0610679
Description: Parameter space in statistical models is considered from the point of view of algebraic geometry and Groebner bases. Estimation of covariance matrix.
Availability: hardcopy
Likelihood ratio tests and singularities
arXiv:math.ST/0703360
Description: A mixture of analytic (Lipshitz-like conditions) and algebro-geometric approach to the usual statistical stuff.
Drton, Mathias and Sullivant, Seth
Algebraic statistical models
arXiv:math.ST/0703609
Statistica Sinica 17(2007), 1273-1297
Description: A short survey. A unifying definition of algebraic statistical model. Multivariate normal distribution in this context is discussed.
Availability: hardcopy
Drucker, Daniel
Exceptional Lie Algebras and the Structure of Hermitian Symmetric Spaces
Memoirs of the American Mathematical Society, No. 208, 1978 (?)
Availability: $26 on amazon
Drutu, Cornelia and Sapir, Mark
Tree-graded spaces and asymptotic cones of groups
arXiv:math/0405030
Topology 44 (2005), No.5, 959-1058
Zentralblatt: 1101.20025
Description: The statement that if a group does not satisfy an identity than it contains a free subgroup appears as Lemma 6.16.
Du, Hong
Automorphism group of Lie algebra $\Bbb C(t)\frac{d}{dt}$
J. Syst. Sci. Complex. 16 (2003), no. 2, 209--212.
Du, Yu and Chen, Xiao-Wu and Ye, Yu
On graded bialgebra deformations
arXiv:math.QA/0506030
Algebra Colloquium, Vol. 14, No. 2 (2007) 301-312
Description: Related to appropriate graded cohomology.
Dubisch, R.
The Wedderburn structure theorems
DOI: 10.2307/2305346
Am. Math. Mon. 54, 253-258 (1947)
Zentralblatt: 0029.10702
Description: Pretty elementary expositions of the rudimenst of the theory of associative and nonassociative algebras, nothing particularly interesting.
Availability: 1947-wedderburn.pdf
Dubisch, Roy and Perlis, Sam
On total nilpotent algebras
Amer. J. Math. 73 (1951), No.2. 439-452
Description: Every associative nilpotent algebra is a subalgebra of an algebra of upper-triangular matrices. Results about their automorphisms, derivations and ideals.
Availability: mathpdf.pdf
Dubois-Violette, M.
d^N = 0
arXiv:q-alg/9710021
Generalized homologies for d^N=0 and graded q-differential algebras
Secondary Calculus and Cohomological Physics (ed. M.Henneaux, J.Krasilshchik and A.Vinogradov), Contemp. Math. 219 (1998)
Description: A survey.
Availability: 97-59.ps
Dubois-Violette, Michel and Hennaux, Marc
Generalized cohomology for irreducible tensor fields of mixed Young symmetry type
Preprint, 1999
Availability: 99-56.ps
Tensor fields of mixed Young symmetry type and N-complexes
math.QA/0110088
Description: Some complexes (of geometrical flavor) and their homology are considered involving Young diagrams. Some mapping between Young diagrams.
Dubrovin, B.A.
Teta-funkcii i nelineinye uravneniya
URL: http://techlibrary.ru/books.htm http://www.newlibrary.ru/book/dubrovin_b_a_/tyeta-funkcii_i_nelineinye_uravnenija.html http://lib.prometey.org/?id=14686&page=2
UMN 36 (1981), N2, 12-
Availability: teta.djvu
Dubrovin, B.A. and Krichever, I.M. and Novikov, S.P.
Integrable Systems. I
Dynamical Systems IV, Encycl. Math. Sci., Vol. 4, Springer, 137-
Sovremennye problemy matematiki. Fundamentalnye napravleniya, VINITI, Vol. 4, 1985, 179-285
Availability: dynsyst-4.djvu (whole volume)
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Dubrovin, B.A. and Novikov, S.P.
Hydrodynamics of soliton lattices
Sov. Sci. Rev. C. Math. Phys. 9 (1993), 1-136
Description: Poisson brackets.
Availability: Dubrovin-Novikov_Hydrodynamics-Soliton-Lattices-1993.pdf
Dubrovin, B.A. and Novikov, S.P. and Fomenko, A.T.
Modern Geometry. Methods and Applications
2nd ed., Nauka, 1986 (in Russian); hardcover, 759 pp.
Availability: hardcopy (book); newer edition available in Kolkhoz; google books
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Duchamp, G. and Thibon, J.Y.
Le support de l'algebre de Lie libre
1989
Availability: hardcopy
Duff, Ana
Invariant forms of the elementary unitary Lie superalgebra
DOI: 10.1016/S0022-4049(03)00071-9
J. Pure Appl. Algebra 184 (2003), no.1, 59-76
Abstract: Invariant forms of toral K-graded Lie superalgebras and, in particular, of the elementary unitary Lie superalgebra over a superring K containing 1/2.
Availability: science.pdf
Derivations of orthosymplectic Lie superalgebras
URL: http://mathematik.uibk.ac.at/mathematik/jordan/archive/duff/index.html http://search.ebscohost.com/login.aspx?direct=true&db=aph&AN=10113342&site=ehost-live
Comm. Algebra 31 (2003), no.6, 2675-2705
arXiv:math.RA/0209139
Availability: hardcopy
Dufour, Jean Paul and Zung, Nguyen Tien
Poisson Structures and Their Normal Forms
DOI: 10.1007/b137493
Birkhauser, 2005, 324 p
Description: Poisson cohomology, Lie algebras cohomology, spectral sequences, Lie algebroids, compatible Poisson structures, normal forms of Poisson structures.
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Dugas, Manfred and Go"bel, Ru"diger
All infinite groups are Galois groups over any field
DOI: 10.2307/2000718
Trans. AMS 304 (1987), No.1, 355-384
Availability: 1987-galois.pdf; hardcopy
Automorphism groups of fields
Manuscripta Mathematica 85 (1994), 227-242
Availability: hardcopy
Duistermaat, H.
Pecularities in the development of the theory of Lie groups
Analysis, et cetera, Academic Press, 1990, 263-282
Description: An interesting historic account.
Availability: CWI
Dukkipati, Ambedkar
Maximum Entropy in the framework of Algebraic Statistics: A First Step
cs.IT/0701117
Abstract: Algebraic statistics is a recently evolving field, where one would treat statistical models as algebraic objects and thereby use tools from computational commutative algebra and algebraic geometry in the analysis and computation of statistical models. In this approach, calculation of parameters of statistical models amounts to solving set of polynomial equations in several variables, for which one can use celebrated Grobner basis theory.
Dula, G.
The interchanging sequence between tensor, Tor and homology
Acta Math. Acad. Sci. Hung. 35, 237-247 (1980)
Zentralblatt: 0461.55015
Description: Some generalities related to the Mayer-Vietoris spectral sequence.
Dumas, Jean-Guillaume and Elbaz-Vincent, Philippe and Giorgi, Pascal and Urbanska, Anna
Parallel computation of the rank of large sparse matrices from algebraic K-theory
arXiv:0704.2351
PASCO'07, 43--52, ACM, New York, 2007
Description: Dealing with large sparse matrices arising in computations of some groups homology.
Availability: hardcopy
Dumas, Jean-Guillaume and Fousse, Laurent and Salvy, Bruno
Compressed Modular Matrix Multiplication
arXiv:0803.1975
Abstract: We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly accessible but modular dot product can be performed by an integer multiplication by the reverse integer. Modular multiplication by a word containing a single residue is a also possible. Therefore matrix multiplication can be performed on such a compressed storage. We here give bounds on the sizes of primes and matrices for which such a compression is possible. We also explicit the details of the required compressed arithmetic routines.
Dumas, Jean-Guillaume and Gautier, Thierry and Giorgi, Pascal and Pernet, Cl\'{e}ment
Dense linear algebra over finite fields: the FFLAS and FFPACK packages
arXiv:cs.SC/0601133
Description: Approach to numerical linear algebra through reduction over finite fields.
Dumas, Jean-Guillaume and Giorgi, Pascal and Pernet, Clement
FFPACK: Finite field linear algebra package
Proc. ISSAC-2004, ACM, 2004, 119-
Description: Description of package(s) achieving matrix manipulations over finite field with the same speed as numerical ones (as in LAPACK).
Availability: page119.pdf
Dumas, Jean-Guillaume and Heckenbach, Frank and Saunders, David and Welker, Volkmar
Computing simplical homology based on efficient Smith normal form algorithms
Algebra, Geometry and Software Systems (ed. Michael Joswig and Nobuki Takayama), Springer, 2003, 177-206
Availability: hardcopy
Dumas, Jean-Guillaume and Saunders, B.D. and Villard, G.
Integer Smith form via the Valence: experience with large matrices from homology
ISSAC 2000, ACM
Availability: hardcopy
Dumas, Jean-Guillaume and Villard, Gilles
Computing the rank of large sparse matrices over finite fields
Availability: hardcopy
Dumas, David
Linear algebraic groups
Thesis, August 2000
Description: Expository: general techniques, classifications, examples, including Lie algebra of algebraic group. .
Availability: mthesis.pdf
Dumas, F.
Hautes derivations et anneaux de series formelles discrete non commutatifs en caracteristique zero
CRAS 303(1986), N19, 943-946
Sous corps complets des corps gauches de series de Laurent a hautes derivations
in: ANNEAUX ET MODULES, Actes colloque Franco belge. Colmar 1991 (ed. Michel GOZE)
Collection Travaux en cours 51. Hermann 1996
Description: higher derivations
Dumont, Jeffrey P. and Reiter, Clifford A.
Visualizing generalized 3x+1 function dynamics
Computers & Graphics 25(2001), N5, 883-898
Availability: science.pdf
Duncan, A.J. and Ellis, Graham J. and Gilbert, N.D.
A Mayer-Vietoris sequence in group homology and the decomposition of relation modules
Glasg. Math. J. 37 (1995), No.2, 159-171
Zentralblatt: 0836.55010
Description: An exact sequence relating a low-degree group cohomology of F/N, F/M and F/MN (F - free).
DuPre', A.M.
Combinatorial extension cohomology. I: Groups
Adv. Math. 106 (1994), No.1, 96-117
MR 96a:20074
Zentralblatt: 0846.20055
Description: An interesting approach to the Lyndon-Hochschild-Serre spectral sequence, allowing to get not only the terms in filtration of H^*, but how they are tight together. The same approach should be valid in the case of factorizable groups (G = AB).
Availability: hardcopy
Durnev, V.G.
On elementary theories of integer linear groups
DOI: 10.1070/IM1995v059n05ABEH000040
Izvestiya Russ. Acad. Sci. 59 (1995), N5, 41-59
MR 1360633
Zentralblatt: 0872.03022
Availability: dur05905.ps
On some subgroups of Fuchsian groups
Questions of group theory and homological algebra, 1998, 69-77
Zentralblatt: 0992.20035
Description: Tits' alternative for some class of groups, and when they are satisfy a nontrivial identity.
Durov, Nikolai and Meljanac, Stjepan and Samsarov, Andjelo and Skoda, Zoran
A universal formula for representing Lie algebra generators as formal power series with coefficients in the Weyl algebra
DOI: 10.1016/j.jalgebra.2006.08.025
arXiv:math.RT/0604096
J. Algebra 309 (2007), N1, 318-359
MR 2301242 (me)
Description: Deformations of U(L) inside Weyl algebra.
Availability: hardcopy
Durvye, Clémence and Lecerf, Grégoire
A concise proof of the Kronecker polynomial system solver from scratch
DOI: 10.1016/j.exmath.2007.07.001
Expositiones Mathematicae Volume 26, Issue 2, 5 May 2008, Pages 101-139
Description: A "black box" approach to solution of polynomial equations, radically different from Grobner bases technique.
Duzhin, F.S.
Lower estimates for a number of closed trajectories of generalized billiards
PhD Thesis, Royal Inst. Technology, Stockholm, 2005; paperback, 66 pp.
Availability: hardcopy
Duzhin, S.V.
A spectral sequence associated with a foliation, and Gelfand-Fuks cohomology of certain Lie algebras of vector fields
Russian Math. Surveys 39(1984), N1, 147-148
UMN 39(1984), N1, 135--136
Dwyer, W.G.
Homotopy Theoretic Methods in Group Cohomology
Birkhauser, 2002, 112p
Availability: $29.95
Dwyer, W.G. and Greenlees, J.P.C. and Iyengar, S.
Duality in algebra and topology
Advances in Mathematics Volume 200, Issue 2 , 1 March 2006, Pages 357-402
Abstract: We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincare' duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson-Carlson duality for cohomology rings of finite groups, (4) Poincare' duality for groups and (5) Gross-Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon.
Dyer, Eldon and Roitberg, Joseph
Note on Sequences of Mayer-Vietoris Type
Proceedings of the American Mathematical Society, Vol. 80, No. 4. (Dec., 1980), pp. 660-662.
Description: Sheer homotopy.
Availability: 0-150.pdf
Dynkin, E.B.
The structure of semi-simple algebras
UMN, 1947, Volume 2, Issue 4(20), Pages 59-127
AMS Transl. 17 (1950), 153 pp.
MR 27752
Selected Papers of E.B. Dynkin With Commentary
AMS, 2000; hardcover, 798 pp.
Availability: hardcopy (book)
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Dyson, Freeman J.
Missed Opportunities
Bull. Amer. Math. Soc. 78 (1972), 635-
Dzhumadildaev, Askar
On deformations of classical simple Lie algebras (in Russian)
UMN 31 (1976), 211-212
Description: Parametric family of 10-dimensional deformations of B_2 over p=3.
Availability: hardcopy
Deformations of the general Lie algebras of Cartan type
Sov. Math. Dokl. 21 (1980), 605-609
Zentralblatt: 0454.17009
Availability: hardcopy
Relative cohomology and deformations of Lie algebras of Cartan type
Sov. Math. Dokl. 23 (1981), 398-402
Zentralblatt: 0467.17010
Availability: hardcopy
A remark on the space of invariant differential operators
Moscow Univ. Math. Bull. 37 (1982), N2, 63-68
On the cohomology of modular Lie algebras
DOI: 10.1070/SM1984v047n01ABEH002634
Math. USSR-Sb 47 (1984), N1, 127-143
MR 83m:17008
Zentralblatt: 0504.17006
Description: Proposition 1: a "pedestrian" but interesting proof of invariance of cohomology under the torus actions. H^1 of Zassenhaus algebra in irreducible modules.
Availability: hardcopy; sm_47_127.pdf
Irreducible representations of strongly solvable Lie algebras over a field of positive characteristic
DOI: 10.1070/SM1985v051n01ABEH002855
Mat. Sb. 123 (1984), No.2, 212-229
Zentralblatt: 0542.17004
Description: Universal p-envelope. Theorem 3: over an algebraically closed field, the class of supersolvable (i.e. having composition factors with all codimensions 1) and strongly solvable (i.e. [L,L] is nilpotent) Lie algebras coincide.
Availability: hardcopy
Central extensions and invariant forms of Cartan type Lie algebras of positive characteristic
Funct. Anal. Appl. 18 (1984), 331-332
MR 86j:17016
Zentralblatt: 0569.17005
Description: Embedding H^2(L,K) -> H^1(L,L^*).
Availability: hardcopy
Central extensions of the Zassenhaus algebra and their irreducible representations
DOI: 10.1070/SM1986v054n02ABEH002980
Mat. Sbornik 126 (1985), N4, 473-489
MR 86j:17017
Description: Relation of complexes C^*(L,K) and C^*(L,L^*)
Availability: hardcopy
Simple Lie algebras with a subalgebra of codimension one
Russian Math. Surv. 40 (1985), no.1, 215-216
Description: Including the case p=2.
Availability: hardcopy
Abelian extensions of modular Lie algebras
DOI: 10.1007/BF01978701
Algebra Logic 24 (1985), 1-7; Correction: 28 (1989), No.2, 162
MR 87c:17019
Zentralblatt: 0586.17008 0694.17010
Description: H^2 of Zassenhaus algebra in irreducible modules.
Availability: hardcopy; 1985-abelian.pdf; 1985-abelian-correction.pdf
2-cohomology of a nilpotent subalgebra of the Zassenhaus algebra
Izv. Vyssh. Uchebn. Zaved. Mat. 1986, no.2, 59-61
MR 87i:17013
Description: Conjecture about stabilization of the whole cohomology for large p.
Availability: hardcopy
Generalized Casimir elements
DOI: 10.1070/IM1986v027n02ABEH001182
Math. USSR Izv. 27 (1986), 391-400
MR 87g:17014
Zentralblatt: 0602.17007
Description: Conjecture: for a finite-dimensional Lie algebra over p>0, every element in Z(U(L)) is a generalized Casimir element.
Availability: im_27_391.pdf
On a Levi theorem for Lie algebras of characteristic p
DOI: 10.1070/RM1986v041n05ABEH003434
Rus. Math. Surv. 41 (1986), N5, 139-140
MR 88c:17016
Zentralblatt: 0612.17012
Description: H^2(L,M) not 0 for any modular Lie algebra and some module M, and the number of such modules is finite.
Availability: hardcopy; rm_41_139.pdf
Integral and mod p-cohomologies of the Lie algebra W_1
DOI: 10.1007/BF01077629
Funct. Anal. Appl. 22 (1988), No.3, 226-228
Zentralblatt: 0658.17011
Description: H^3, H^4; relationship between cohomology over Z and Z_p. Relationship between cohomology of a Lie algebra and its subalgebra of codimension 1.
Availability: hardcopy; 1988-integral.pdf
Deformations of the Lie algebras W_n(m)
DOI: 10.1070/SM1990v066n01ABEH001313
Math. USSR Sb. 66 (1990), No.1, 169-187
Zentralblatt: 0691.17009
Description: H^2(W_n(m),W_n(m)); more precise relationship between filtered and generic deformations (via specialization of parameters) (Theorem 2).
Availability: hardcopy
Cohomology of truncated coinduced representations of Lie algebras of positive characteristic
DOI: 10.1070/SM1990v066n02ABEH001317
Math. USSR Sb. 66 (1990), No.2, 461-473
Zentralblatt: 0691.17008
Availability: hardcopy
Central extensions of infinite-dimensional Lie algebras
DOI: 10.1007/BF01075045
Funct. Anal. Appl. 26 (1992), no.4, 247-253
MR 94b:17035
Zentralblatt: 0797.17013
Availability: hardcopy
Cohomology and nonsplit extensions of modular Lie algebras
Contemporary Math. 131, Part 2 (1992), 31-43
MR 93f:17034
Zentralblatt: 0774.17026
Zbl Review: Any Lie algebra of prime characteristic has at least one non-split extension and the number of irreducible modules with such a property is finite. On the other hand, any solvable extension of Lie algebras can be imbedded in some split extension with kernel whose index of solvability will be the same as the index of the given extension kernel. A similar thing holds for extensions of modules. These facts are corollaries for general cohomological results about existence of the cohomological functor in the category of finite dimensional modules and algebras. It gives all nonsplit extensions of simple restricted Lie algebras of rank one $(\text{sl}\sb 2,W\sb 1(1),H\sb 2(1,1))$ and Lie algebra of Cartan type $W\sb 2(1,1)$ by an irreducible module.
Availability: hardcopy (book)
Quasi-Lie bialgebra structures of sl_2, Witt and Virasoro algebras.
Israel Math. Conf. Proc. 7 (1993), 13-24
MR 95a:17034
Zentralblatt: 0852.17013
Availability: hardcopy (book)
Derivations and central extensions of the Lie algebra of formal pseudodifferential operators.
Algebra i Analiz 6 (1994), no.1, 140-158
St. Petersburg Math. J. 6 (1995), no.1, 121-136
MR 95d:17021
Odd central extensions of Lie superalgebras
Funct. Anal. Appl. 29 (1995), No.3, 202-204
Zentralblatt: 0869.17021
Availability: hardcopy
Virasoro type Lie algebras and deformations
DOI: 10.1007/s002880050272
Z. Phys. C 72 (1996), no.3, 509-517
MR 97j:17030
Zentralblatt: 0935.17012
Description: Deformations of Hamiltonian (inf.dim.) Lie alg.
Availability: hardcopy; gk_mp_9512_25.dvi
Cohomology and deformations of semidirect sums of Lie algebras.
Dokl. Akad. Nauk 355 (1997), no.5, 586-588
none
Zentralblatt: 0978.17012
Availability: hardcopy
Symmetric (co)homologies of Lie algebras
CRAS 324 (1997), 497-502
MR 98c:17019
Abstract: Cohomologies of Lie algebras are usually calculated using the Chevalley-Eilenberg cochain complex of skew-symmetric forms. We consider two cochain complexes consisting of forms with some symmetric properties. First, cochains C*(L) are symmetric in the last 2 arguments, skew-symmetric in the others and satify moreover some kind of Jacobi condition in the last 3 arguments. In characteristic 0, its cohomologies are isomorphic to the cohomologies of the factor-complex C* (L, L´)/C*+1 (L, K). Second, a symmetric version C*«lambda»(A) is defined for an associative algebra A . It is a subcomplex of the cyclic cochain complex. These symmetric cochain complexes are used for the calculation of 3-cohomologies of Cartan Type Lie algebras with trivial coefficients.
Availability: hardcopy
Cohomologies and deformations of right-symmetric algebras
DOI: 10.1007/BF02366344
J. Math. Sci. 93 (1999), N6, 836-876
Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 55, Algebra-11, 1998
arXiv:math.DG/9807065
Cohomologies of colour Leibniz algebras: pre-simplicial approach.
Lie Theory and Its Applications in Physics, III, World Sci., 2000, 124-136
Availability: TUDelft: CB P-EC2000; absent in Iceland, VU, UVA, CWI.
Minimal identities for right-symmetric algebras
DOI: 10.1006/jabr.1999.8109
J. Alg. 225 (2000), 201-230
arXiv:math.RT/9809082 (differs from the journal version)
Description: Analogues of Witt algebras. Identities for them are derived from the Amitsur-Levistki identity via a certain functor from the author's Moscow Univ. Math. Bull. 1982 paper.
Availability: hardcopy
Jacobson formula for right-symmetric algebras in characteristic p
Special issue dedicated to Alexei Ivanovich Kostrikin. Comm. Algebra 29 (2001), no. 9, 3759-3771
Availability: hardcopy
Novikov-Jordan algebras
DOI: 10.1081/AGB-120015649
Comm. Algebra 30 (2002), no.11, 5207-5240
arXiv:math.RA/0202044
Identities and derivations for Jacobian algebras
Quantization, Poisson brackets and beyond, Contemp. Math. 315 (2002), 245-278
arXiv:math.RA/0202040
Description: n-Poisson structures.
N-commutators
DOI: 10.1007/s00014-004-0807-2
Comm. Math. Helv. 79 (2004), N3, 516-553
arXiv:math.RA/0203036
Zentralblatt: (me)
Description: n-commutator [x_1, ..., x_n] is defined as \sum_{sigma in S(n)} sign(sigma) x_{sigma(1), ..., x_sigma(n)}. Theory of n-commutators with emphasis of Lie algebras of vector fields is developed. Related to identities of the Witt algebra.
Availability: hardcopy
q-chronological algebras
Doklady Math. 71 (2005), No. 2, 264-
n-Lie structures that are generated by wronskians
DOI: 10.1007/s11202-005-0061-7
Siberian Math. J. 46 (2005), N4, 601-612
Description: Low characteristics exhibiting some special phenomena are involved.
Zinbiel algebras over a q-commutator
Fundam. Prikl. Mat. 11 (2005), no. 3, 57--78 (in Russian)
The n-Lie property of the Jacobian as a condition for complete integrability
DOI: 10.1007/s11202-006-0075-9
Siber. Math. J. 47 (2006), N4, 643-652
Description: Involved an associative commutative algebra with a system of derivations.
10-commutators, 13-commutators and odd derivations
J. Nonlinear Math. Phys. 15 (2008), no.1, 87--103
arXiv:math-ph/0603054
$q$-Leibniz algebras
Serdica Math. J. 34 (2008), no. 2, 415--440
Description: a*b = ab + qba.
Dzhumadildaev, Askar and Abdykassymova, Saule A.
Leibniz algebras in characteristic p
Comptes Rendus Acad. Sci. 332 (2001), N12, 1047-1052
Zentralblatt: pre01657730
Abstract: We give the definition of restrictness for Leibniz algebras in characteristic p . We prove that the cohomology of Leibniz algebras with coefficients in an irreducible module is trivial, if the module is not restricted. The number of irreducible antisymmetric modules with nontrivial cohomology is finite. A Leibniz algebra is called simple, if it has no proper ideal except ideal generated by squares of it