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Aarseth, Sverre J.
Direct methods for N-Body simulations
DOI: 10.1007/3-540-57983-4_22
Galactic Dynamics and N-Body Simulations, Lect. Notes Phys. 433 (1994), 275-312
Abarbanel, Joseph
On commutator ideals in free Lie algebras
DOI: 10.1016/j.jalgebra.2004.02.039
J. Algebra 296 (2006), no.2, 323--338
Abstract: Let L be a free Lie algebra over a field k, I and J non-trivial proper ideals of L. If I+J not L then the Schur multiplier H_2(L/[I,J],k) of L/[I,J] is not finite dimensional, and so in particular, L/[I,J] is not finitely presented.
Abarbanel, Joseph and Rosset, Shmuel
Some non-finitely presented Lie algebras
J. Pure Appl. Alg. 127 (1998), no.2, 105-112
arXiv:math.GR/9611204
MR 99c:17034
Zentralblatt: 1017.17016
Description: Let L be a free Lie algebra, I an ideal of L. H_2(L/I^n) is not finitely generated, and so in particular, L/I^n is not finitely presented, even when L/I is finite dimensional. The technique is some embedding of H_2 into modules over U(L).
Availability: hardcopy
Abdelmalek, M.A. and Leng, X. and Patera, J. and Winternitz, P.
Grading refinements in the contraction of Lie algebras and their invariants
J. Phys. A: Math. Gen. 29 (1996), 7519-7543
Abdollahi, Alireza
A combinatorial problem in infinite groups
arXiv:math.GR/0212017
Bull. Malaysian Math. Soc. 2002
Description: Results about a variety of groups in which each finite group is nilpotent.
Abdulrab, Habib and Goralcik, Pavel and Makanin, G. S.
Functions for the general solution of parametric word equations
DOI: 10.1007/3-540-63045-7_20
Lect. Notes Comp. Sci. 1234 (1997), 189-202
Zentralblatt: 0892.20034
Description: Certain specific equations in a free monoid.
Availability: 1997-functions.pdf
Abdykasymova, S. A.
The Leibniz 2-cohomology of the nilpotent subalgebra of the Zassenhaus algebra
Izv. Minist. Obraz. Nauki Nats. Akad. Nauk Resp. Kaz. Ser. Fiz.-Mat. 2000, no. 3, 8--14
Abdykhalykov, A. T. and Mikhalev, A. A. and Umirbaev, U. U.
Automorphisms of two-generated free Leibniz algebras.
Comm. Algebra 29 (2001), no. 7, 2953--2960.
Zentralblatt: 0978.17001
Ablamowicz, Rafal and Fauser, Bertfried
Mathematics of CLIFFORD - A Maple package for Clifford and Grassmann algebras
math-ph/0212031
Adv. Appl. Clifford Algebr. 15 (2005), no. 2, 157--181
Aboughazi, Rachida
Restricted homology of p-Lie algebras of degree two
Ann. Inst. Fourier 39 (1989), N3, 641-649
Description: Restricted homology H_2 (sl_n(A))
Aboughazi, R. and Ogle, C.
On Chevalley-Eilenberg and cyclic homologies
DOI: 10.1006/jabr.1994.1154
J. Algebra 166 (1994), no. 2, 317--339
MR 95f:19002
Abstract: The first purpose of this paper is to give a new proof of the Loday-Quillen-Tsygan theorem which establishes an isomorphism of graded commutative Hopf algebras between the Chevalley-Eilenberg homology $H^L_*({\rm gl}(A))$ of the Lie algebra ${\rm gl}(A)$ and the symmetric algebra $S(HC_{*-1}(A))$ of the cyclic homology of $A$, where $A$ is an algebra with unity over a field of characteristic $0$. The argument used here is based on a result which holds for subcomplexes $D_*$ of the Chevalley-Eilenberg complex $\Lambda^*({\rm gl}(A))$, with minimal conditions on $D_*$: the case where $D_*=\Lambda^*({\rm gl}(A))$ implies directly the above Loday-Quillen-Tsygan theorem. Then the authors apply their method to the computation of the homology of other Lie algebras: they consider in particular the Lie algebra ${\rm sl}(A)$ and its universal central extension ${\rm st}(A)$ and obtain the following (not surprising) isomorphisms: $H^L_*({\rm sl}(A))\cong S(HC^{(1)}_{*-1}(A))$ and $H^L_*({\rm st}(A))\cong S(HC^{(2)}_{*-1}(A))$, where $HC^{(i)}_*(A)=HC_*(A)$ for $*\geq i$ and $HC^{(i)}_*(A)=0$ for * < i. Finally, they calculate the Leibniz algebra homology of the Leibniz algebras obtained from the Lie algebras gl(A), sl(A), st(A), by forgetting the antisymmetry of the bracket.
Availability: 1994-chevalley.pdf
Abramovskii, I. N.
Locally generalized Hamiltonian groups
Siberian Mathematical Journal Issue: Volume 7, Number 3 May 1966 Pages: 391 - 393
Abramson, Bruce and Yung, Mordechai M.
Divide and conquer under global constraints: a solution to the N-queens problem
DOI: 10.1016/0743-7315(89)90011-7
J. Parallel and Distributed Computing 6 (1989), 649-662
Availability: 1989-divide.pdf
Abreu, E.M.C. and Dalmazi, D. and Silva, E.A.
The Jacobi identity for Dirac-like brackets
Int. J. Mod. Phys. A 17, No.3, 395-404 (2002)
Zentralblatt: 0994.81052
Acton, F.S.
Analysis of Straight-Line Data
Wiley, 1959; hardcover, 267 pp.
Availability: hardcopy (book)
Aczel, J.
Lectures on Functional Equations and Their Applications
AP, 1966
Availability: a_el1810.djvu
Aczel, J. and Dhombres, J.
Functional Equations in Several Variables
Fizmatlit, 2003
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Aczel, J. and Forte, B. and Ng, C. T.
Why the Shannon and Hartley entropies are 'natural'
DOI: 10.2307/1426210
Adv. Appl. Probab. 6 (1974), No.1, 131-146
Availability: 1974-shannon.pdf
Ada'mek, Jir(i' and Sobral, Manuela and Sousa, Lurdes
Morita equivalence of many-sorted algebraic theories
Journal of Algebra Volume 297, Issue 2 , 15 March 2006, Pages 361-371
Abstract: Algebraic theories are called Morita equivalent provided that the corresponding varieties of algebras are equivalent. ... we prove that all theories Morita equivalent to an S-sorted theory T are obtained as idempotent modifications of T. This is analogous to the classical result of Morita that all rings Morita equivalent to a ring R are obtained as idempotent modifications of matrix rings of R.
Adamovic, Drazen
Representations of the vertex algebra W_1+\infty with a negative integer center charge
Comm. Alg. 29 (2001), N7, 3153-3166
Availability: 100105014.pdf
Adams, J.F.
Review of "Algebraic K-Theory" by Hyman Bass
BLMS 1970 (?), 233-238
Availability: hardcopy
Infinite Loop Spaces
Princeton Univ. Press, 1978; paperback, 214 pp.
Availability: hardcopy (book)
Lectures on Exceptional Lie Groups
The Univ. of Chicago Press, 1996
Availability: Kolkhoz
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Adams, J. F. and Lax, Peter D. and Phillips, Ralph S.
On Matrices Whose Real Linear Combinations are Nonsingular
Proceedings of the American Mathematical Society, Vol. 16, No. 2 (Apr., 1965), pp. 318-32l; correction: 17 (1966), 945947
Description: Maximal dimension of such space of matrices (over R).
Availability: 2033871.pdf
Adem, Alejandro and Karoubi, Max
Periodic cyclic cohomology of group rings
URL: http://www.math.jussieu.fr/~karoubi/PCCGR.pdf http://www.mathematik.uni-osnabrueck.de/K-theory/0102/paper.ps.gz
DOI: 10.1016/S0764-4442(97)82705-X
CRAS 326 (1998), 13-17
Adem, Alejandro and Milgram, R. James
Cohomology of Finite Groups, 2nd ed.
Springer, 2004, 383 p.
Availability: 73 EUR at Lange and Sringer
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google books
Adem, Alejandro and Naffah, N.
On the Cohomology of SL_2(Z[1/p])
London Mathematical Society Lecture Note Series 252, pp. 1-9 (1998)
Adian, S.I (=Adyan)
Problema Bernsaida v periodicheskikh gruppakh i smezhnye voprosy
Sovr. Probl. Matematiki 1 (2003), 5-
Description: An interesting (and opinionated) survey.
Availability: hardcopy (pages 18 and 19 only)
Adian, S.I. (=Adyan) and Durnev, V.G.
Algoritmicheskie problemy dlya grupp i polugrupp
UMN 55 (2000), N2, 3-94
Description: A survey.
Availability: adyan2u.ps
Adian, S.I. and Grunewald, F. and Mennicke, J.
On prime quaternions, Hurwits relations and a new operation of group extension
Proc. Steklov Inst. Math. 242 (2003), 3-17
Description: "A new operation of group extension" is adding of new generators with commutation relations between some of them and some of the old ones, imitating some arithmetical phenomena in quaternions.
Availability: hardcopy
Adian, S.I. (=Adyan) and Lysenok, I.G.
On groups all of whose proper subgroups are finite cyclic
URL: http://www.iop.org/EJ/abstract/0025-5726/39/2/A01 http://mi.mathnet.ru/eng/izv977
DOI: 10.1070/IM1992v039n02ABEH002232
Math. USSR Izv. 39 (1992), N2, 905-957
MR 1149884
Zentralblatt: 0771.20015
Description: Horrible.
Availability: IZV_39_2_A01.pdf
Adiga, Chandrashekar and Cooper, Shaun and Han, Jung Hun
A general relation between sums of squares and sums of triangular numbers
Int. J. Number Theory 1(2005), No.2, 175-182
Zentralblatt: pre02214599
Availability: S1793042105000078.pdf
Adin, Ron and Blanc, D.
Resolutions of associative and Lie algebras
Canad. Math. Bull. 43 (2000), 3-16.
Description: Some resolution of free algebras are constructed in terms of combinatorial structures; cohomology of free Lie algebra in class of noncommutative algebras; ref. to Quillen's definition of homology in model categories.
Availability: resol6.ps
Adin, R.M. and Frumkin, A. and Roichman, Y.
Hook interpolations
URL: http://www.ingenta.com/isis/searching/ExpandTOC/ingenta;jsessionid=?issue=infobike://ap/ja/2002/00000258/00000002&index=9 http://dx.doi.org/10.1016/S0021-8693(02)00642-7
J. Algebra 258(2002), N2, 543-562; Erratum: 262(2003), N1, 262-264
Abstract: The hook components of V^\otimes n interpolate between the symmetric power Sym^n(V) and the exterior power \wedge^n(V)...
Adjamagbo, Kossivi and Essen, Arno van den
On the equivalence of the Jacobian, Dixmier and Poisson Conjectures in any characteristic
arXiv:math.AG/0608009
Description: Interesting historic notes about Weyl algebras.
Ado, I.D.
Über die Struktur der endlichen kontinuierlichen Gruppen
Bull. Soc. Phys.-Math. Kazan, III. Ser. 6, 38-42 (1934) (in Russian)
Zentralblatt: 0010.39403
Jahrbuch: 58.0440.04
Description: Approach to classification of nilpotent Lie algebras via sequential singling out of the center?
Über die Darstellung von S. Lieschen Gruppen durch lineare Substitutionen
Dokl. Acad. Sci. URSS 1935, No.3, 7-8
Zentralblatt: 0012.24903
Jahrbuch: 61.0474.02
Note on the representation of finite continuous groups by means of linear substitutions
Izv. Fiz.-Mat. Obsch. Kazan Univ. 7 (1934/35), 1-43 (in Russian)
Zentralblatt: 0014.34702
Jahrbuch: 61.1217.02
The representation of Lie algebras by matrices
AMS Transl. 1949, N2, 21 pp.
Uspekhi Mat. Nauk. 2 (1947), N6, 159-173
MR 10,350c
Description: p=0. An improved version of the 1935 paper? ... any nilpotent Lie algebra $L$ is shown to be a homomorphic image of the algebra of derivations of a suitable iterated central extension of $L$. Levi-Malcev is employed.
Agalakov, S.A.
A Lie algebra with a single defining relation need not be residually finite
Math. Notes 51 (1992), No.4, 327-329
Mat. Zametki 51 (1992), No.4, 3-7
Zentralblatt: 0791.17004
Description: If p=0 and L is residually finite Lie algebra, then there do not exist nonzero elements a,b,x in L such that ax=a and bx=b.
Agaoka, Yoshio
On the variety of 3-dimensional Lie algebras
Lobachevskii J. Math. 3 (1999), 5-17
An algorithm to determine the isomorphism classes of 4-dimensional complex Lie algebras
DOI: 10.1016/S0024-3795(01)00473-6
Lin. Algebra Appl. 345 (2002), 85-118
Description: References to (numerous) previous classifications.
Availability: 2002-algorithm.pdf (published version)
Agore, A. L. and Militaru, G.
Crossed product of groups. Applications
arXiv:0805.4077
Abstract: We survey the extensions of a group by a group using crossed products instead of exact sequences of groups. The approach has various advantages, one of them being that the crossed product is an universal object. Several new applications are given, a general Schreier type theorem is proved and a few open problems are left.
Agrachev, A.A. and Gamkrelidze, R.V.
Chronological algebras and nonstationary vector fields
DOI: 10.1007/BF01084595
Problemy Geometrii, Vol. 11, VINITI, 1980, 135-176
Journal of Mathematical Sciences Volume 17, Number 1 / September, 1981 Pages 1650-1675
Description: Algebras with condition [L_x,L_y] = L_[x,y] (L_x - left multiplication on x) what is equivalent to x(yz) - y(xz) = (xy - yx)z.. Their relation with Lie algebras.
Availability: problemy-geometrii-11.djvu (whole book)
Agrachev, Andrei A. and Liberzon, Daniel
Lie-algebraic stability criteria for switched systems
SIAM J. Control Optim. 40 (2001), N1, 253-269
Description: At the very end, it is proved that the set of 2-generators of gl_n(R) is dense in gl_n(R) x gl_n(R)
Availability: agrachev.ps
Agrebaoui, B. and Ammar, F. (=Ben Ammar) and Ben Fraj, N. and Ovsienko, V.
Deformations of modules of differential forms
math.QA/0310494
J. Nonlinear Math. Phys., volume 10, no. 2 (2003) 148-156
Agrebaoui, B. and Ammar, F. and Lecomte, P.
On the cohomology of the spaces of differential operators acting on skewsymmetric tensor fields or on forms, as modules of the Lie algebra of vector fields
math.DG/0208251
Diff. Geom. Appl. 20(2004), N2, 241-249
Zentralblatt: 1038.17017 (me)
Availability: hardcopy
Agrebaoui, B. and Ammar, F. and Lecomte, P. and Ovsienko, V.
Multi-parameter deformations of the module of symbols of differential operators
DOI: 10.1155/S1073792802101127
Int. Math. Res. Not. 2002, no. 16, 847--869.
MR 2003a:17030 (Rutwig)
Zentralblatt: (me)
Availability: hardcopy
Agrebaoui, B. and Ben Fraj, N.
On the cohomology of the Lie superalgebra of contact vector fields on $S^{1|1}$
Bull. Soc. R. Sci. Li\`ege 72, No.6, 365-375 (2003)
Zentralblatt: (me)
Availability: hardcopy
Agrebaoui, Boujemaa and Ben Fraj, Nizar and Omri, Salem
Deforming the Lie superalgebra of contact vector fields on S^{1|1}
math-ph/0603058
J. Nonlinear Math. Phys. 13 (2006) no. 1, 19--33
On the cohomology of the Lie superalgebra of contact vector fields on S^{1|2}
math-ph/0603057
J. Nonlinear Math. Phys. 13 (2006), no. 4, 523--534
Description: First cohomology.
Aguiar, Marcelo
Pre-Poisson algebras
DOI: 10.1023/A:1010818119040
Lett. M. Phys. 54 (2000), 263-277
Description: Pre-Lie + zinbiel structure.
On the associative analog of Lie bialgebras
DOI: 10.1006/jabr.2001.8877
J. Algebra 244 (2001), no.2, 492-532
Description: Relation with low-dimensional cyclic cohomology.
Availability: science.pdf
Ahad, R. and Yao, B.
RQL: a recursive query language
IEEE Trans. Knowledge and Data Engineering 5(1993), N3, 451-461
Availability: 00224197.pdf
Ahrens, H.
Varianzanalyse
Akademie-Verlag, Berlin, 1967; small format, paperback, 198 pp.
Availability: hardcopy (book)
Airault, Helene and Ren, Jiagang
An algebra of differential operators and generating functions on the set of univalent functions
Bull. Sci. Math. 126(2002), 343-367
Zentralblatt: (me)
Availability: hardcopy
Aivazis, M.
Group Theory in Physics. Problems and Solutions
1st reprint, World Scientific, 1995; paperback, 111 pp.
Availability: hardcopy (book)
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Akaike, Hirotugu
A new look at the statistical model identification
IEEE Transactions on Automatic Control Dec 1974 Volume: 19, Issue: 6 page(s): 716- 723
Description: Seems to be a classical paper where AIC was introduced.
Availability: 1974-new.pdf
A new look at the Bayes procedure
DOI: 10.1093/biomet/65.1.53
Biometrika 1978 65(1):53-59
Availability: 53.pdf
Factor analysis and AIC Factor analysis and AIC
DOI: 10.1007/BF02294359
Psychometrika Volume 52, Number 3 / September, 1987 Pages 317-332
Availability: 1987-factor.pdf
Akbari, S. and Ebrahimian, R. and Momenaee Kermani, H. and Salehi Golsefidy, A.
Maximal subgoups of GL_n(D)
J. Alg. 259 (2003), 201-225
Availability: sl_nd.pdf
Akbari, S. and Mohammadian, A.
Zero-divisor graphs of non-commutative rings
DOI: 10.1016/j.jalgebra.2005.07.007
J. Algebra 296 (2006), N2, 462-479
Akhavan-Malayeri, M.
Commutator length and square length of the wreath product of a free group by the infinite cyclic group
Houston J. Math. 27 (2001), N4, 753-756
Description: If G is any group and W is the wreath product of G by the infinite cyclic group then every element of W' is a product of at most three commutators, and every element of W2 is a product of at most seven squares in W.
Akhavan-Malayeri, Mehri and Rhemtulla, Akbar
Products of Commutators in Free Groups
International Journal of Algebra and Computation, Vol. 13, No. 2 (2003) 231-240
Akhiezer, N.I. (=Achiezer)
Theory of Approximation
Dover, 1992; paperback, 307 pp.
Availability: hardcopy (book); amazon
Elements of the Theory of Elliptic Functions
2nd ed., Nauka, 1970 (in Russian); hardcover, 304 pp.
Availability: hardcopy (book); amazon; Kolkhoz (Russian edition)
Akhiezer, D.N. and Vinberg, E.B. and Gorbatsevich, V.V. and Durnev, V.G. and Sulanke, R. and Kazarin, L.S. and Leites, D. and Serganova, V. and Tikhomirov, V.M.
Arkadii Lvovich Onishchik (on his 70th birthday)
Rus. Math. Surv. 58(2003), N6, 1245-1253
MR 2054110
Description: Including list of publications.
Availability: hardcopy
Akhmedov, Azer
On the girth of finitely generated groups
DOI: 10.1016/S0021-8693(03)00375-2
J. Algebra 268 (2003), no.1, 198-208
Availability: 1st.pdf; hardcopy
The girth of groups satisfying Tits alternative
DOI: 10.1016/j.jalgebra.2005.01.053
J. Algebra 287 (2005), N2, 275-282
Description: A finitely generated linear group which is not virtually solvable has infinite girth. From this and from Tits alternative follows that a fintely generated linear group has finite girth iff it is virtually solvable.
Availability: science.pdf; hardcopy (preprint version, under the title "On the girth of groups containing free subgroups")
Perturbation of wreath products and quasi-isometric rigidity 1
DOI: 10.1093/imrn/rnn004
Int. Math. Res. Notices 2008, article ID rnn004, 18 pages
Availability: rnn004.pdf
Akin, E.
Why is the 3x+1 problem hard?
Contemp. Math. 356(2004), first article
Akin, Kaan and Buchsbaum, David A. and Weyman, Jerzy
Schur functors and Schur complexes
Adv. Math. 44 (1982), 207-278
MR 84c:20021
Availability: hardcopy
Akman, Fusun
A Characterization of the differential in semi-infinite cohomology
DOI: 10.1006/jabr.1993.1249
J. Algebra 162 (1993), N1, 194-209
On some generalizations of Batalin-Vilkovisky algebras
J. Pure Appl. Alg., to appear
arXiv:q-alg/9506027
Abstract: We define the concept of higher order differential operators on a general noncommutative, nonassociative superalgebra A, and show that a vertex operator superalgebra has plenty of them, namely modes of vertex operators. A linear operator \Delta is a differential operator of order at most r if an inductively defined (r+1)-form \Phi_{\Delta}^{r+1} is identically zero. When A is supercommutative and associative and \Delta is an odd, square zero, second order differential operator on A, \Phi_{\Delta}^2 defines a "Batalin-Vilkovisky algebra" structure on A. We generalize this notion to any superalgebra with an odd, square zero, second order differential operator, and show that all properties of the classical BV bracket but one continue to hold "on the nose". We also point out connections to Leibniz algebras and the noncommutative homology theory of Loday. Taking the generalization process one step further, we remove all conditions on \Delta to examine the changes in the basic properties of the bracket. We see that a topological chiral algebra with a mild restriction yields a classical BV algebra in the cohomology. Finally, we investigate the quantum BV master equation and relate it to deformations of differential graded algebras.
Chicken or egg? A hierarchy of homotopy algebras
arXiv:math.QA/0306145, 32 pages
Description: May be helpful in structures on the cohomology space?
Akman, Fusun and Ionescu, Lucian M. and Sissokho, Papa A.
On deformation theory and graph homology
DOI: 10.1016/j.jalgebra.2006.10.025
math.QA/0507077
J. Algebra 310 (2007), N2, 730-741
Abstract: Deformation theory of associative algebras and in particular of Poisson algebras is reviewed. The role of an almost contraction leading to a canonical solution of the corresponding Maurer-Cartan equation is noted. This role is reminiscent of the homotopical perturbation lemma, with the infinitesimal deformation cocycle as initiator. Applied to star-products, we show how Moyal's formula can be obtained using such an almost contraction and conjecture that the merger operation provides a canonical solution at least in the case of linear Poisson structures.
Akrami, S. E. and Majid, S.
Braided cyclic cocycles and nonassociative geometry
Journal of Mathematical Physics -- October 2004 -- Volume 45, Issue 10, pp. 3883-3911
Description: Braided cyclic homology.
Alam, R. and Bora, Shreemayee
Stability of eigenvalues and spectral decompositions under linear perturbation
Linear Algebra Appl. 364 (2003), 189--211
Alberca Bjerregaard, Pablo and Elduque, Alberto and Martin Gonzalez, Candido and Navarro Marquez, Francisco Jose
On the Cartan-Jacobson theorem
J. Algebra 250, No.2, 397-407 (2002)
Zentralblatt: 1001.17009
Zbl Review: The Cartan-Jacobson theorem states that for characteristic $\ne 2,3$ the Lie algebra of derivations of a Cayley algebra is central simple. The authors show here that this theorem still holds when characteristic $=2$. However, in the case characteristic $=3$, there is a unique 7-dimensional ideal which is a central simple Lie algebra of type $A_2$; and the quotient of the derivation algebra modulo this ideal is isomorphic as a Lie algebra to the ideal itself.
Albert, A. Adrian
Structure of Algebras
AMS, 1939, 210 pp. (republished in 1980?)
MR 1:99c
Availability: VRII 512 Alb
The radical of a non-associative algebra
BAMS (?), circa 1942, 891-
Collected Mathematical Papers. Part II, AMS, 1993, 277-
Description: Relationship betrween properties of a nonassociative algebra and its associative envelope, with emphasis on simple and semisimple algebras.
Availability: hardcopy (book)
The Wedderburn principal theorem for Jordan algebras
Ann. Math. 48 (1947), N1, 1-7
Description: Decompositon into the semidirect sum of semisimple part and radical.
Availability: albert.pdf
Collected Mathematical Papers. Parts I, II
AMS, 1993
Availability: hardcopy
Albert, A.A. and Frank, M.S.
Simple Lie algebras of characteristic p
Univ. Politec. Torino, Rend. Sem. Mat. 14 (1955), 117-139
Collected Mathematical Papers. Part II, AMS, 1993, 621-
Zentralblatt: 0065.26801
Availability: hardcopy (book)
Albert, A.A. and Muckenhoupt, Benjamin
On matrices of trace zero
A. Adrian Albert. Collected Mathematical Papers. Part II, AMS, 1993, 659-
Description: Every matrix of trace zero is a commutator.
Availability: hardcopy (book)
Albeverio, S. and Omirov, B.A. and Rakhimov, I.S.
Classification of 4-dimensional nilpotent complex Leibniz algebras
math.RA/0611831
Albuquerque, Helena and Elduque, Alberto
Engel's theorem for Malcev superalgebras
DOI: 10.1080/00927879408825155
Comm. Algebra 22 (1994), N14, 5689 - 5701
A classification of Mal'tsev superalgebras of small dimensions
DOI: 10.1007/BF02366395
Algebra and Logic 35 (1996), N6, 351-365
Description: Also ordinary Malcev algebras.
Albuquerque, Helena and Majid, Shahn
New approach to octonions and Cayley algebras
Nonassociative Algebra and Its Applications (ed. R.Costa and A.Grishkov), M.Dekker, 2000, 1-7
Availability: oct.tar (page 3 is missing)
google books
Aldrovandi, R. and Andrade, V. C. de and Barbosa, A. L. and Pereira, J. G.
Mass Generation from Lie Algebra Extensions
International Journal of Theoretical Physics 42 (12): 2955-2970, December 2003
Aleev, R.Zh.
Structure constants of simple Lie algebras
Contemp. Math. 131, Part 2 (1992), 3-13
Availability: hardcopy (book)
Alexandroff, P.S.
Elementary Concepts of Topology
Dover, 1961; paperback, 73 pp.
Availability: hardcopy (book)
Aleksandrov, P.S. and Baranovich, T.M. and Golovin, O.N. and Plotkin, B.I.
Aleksandr Gennadievich Kurosh (obituary)
DOI: 10.1070/RM1972v027n01ABEH001367
Rus. Math. Surv. Volume 27 (1972) Number 1, 176-193
Description: Including list if publications.
Availability: hardcopy
Alekseev, M.A. and Glebskii, L.Yu. and Gordon, E.I.
On approximation of groups, group actions, and Hopf algebras
Description: Approximation by finite(-dimensional) objects, ultrafilters, embeddability.
Availability: a-g-g.ps
Alekseev, A. and Meinrenken, E.
Lie theory and the Chern-Weil homomorphism
arXiv:math.RT/0308135, 38 pages
Abstract: We introduce a canonical Chern-Weil map for possibly non-commutative g-differential algebras with connection. Our main observation is that the generalized Chern-Weil map is an algebra homomorphism ``up to g-homotopy''. Hence, the induced map from invariant polynomials to the basic cohomology is an algebra homomorphism. As in the standard Chern-Weil theory, this map is independent of the choice of connection. Applications of our results include: a conceptually easy proof of the Duflo theorem for quadratic Lie algebras, a short proof of a conjecture of Vogan on Dirac cohomology, generalized Harish-Chandra projections for quadratic Lie algebras, an extension of Rouviere's theorem for symmetric pairs, and a new construction of universal characteristic forms in the Bott-Shulman complex.
On the Kashiwara-Vergne conjecture
arXiv:math.QA/0506499
Description: On the theme of the Duflo map S(g) -> U(g). H*(g,S(g)) = H*(g,U(g)).
Alekseev, Anton and Torossian, Charles
The Kashiwara-Vergne conjecture and Drinfeld's associators
arXiv:0802.4300
Description: Some additive-type cohomology for free Lie algebras. Related to Campbell-Baker-Hausdorff formula. Interesting classes of Lie algebras related to free ones.
Alekseevskaya, T.V. and Borovik, A.V. and Gelfand, I.M. and White, N.
Matroid homology
in: The Gelfand Mathematical Seminars, 1997-1999, Birkhauser, 1999
Description: Analogous to Kontsevich's graph homology.
Availability: abgw6.pdf
Alekseevskii, D. V.
Lie groups and homogeneous spaces
DOI: 10.1007/BF01084048
J. Math. Sci. 4 (1975), N5, 483-539
Itogi Nauki i Tekhniki (Algebra. Topologiya. Geometriya), Vol. 11, pp. 37-123, 1974
Description: Including Lie algebras.
Availability: 1974-lie-groups.pdf
Lie groups
DOI: 10.1007/BF02105458
J. Math. Sci. 28 (1985), N6, 924-949
Itogi Nauki i Tekhniki, Ser. Algebra, Topol., Geom., VINITI, Vol. 20, 1982
Description: Including many questions on Lie algebras, especially classical ones.
Availability: 1985-lie-groups.pdf
Alekseevskii, D. V. and Cortes Suarez, Vicente and Devchand, Chandrashekar and Van Proeyen, Antoine
Polyvector super-Poincare algebras
Comm. Math. Phys. 253 (2005), no. 2, 385--422
Alekseevsky, D. and Grabowski, J. and Marmo, G. and Michor, P. W.
Poisson structures on double Lie groups
arXiv:math.DG/9801028
Description: A survey: Lie bialgebras, metric Lie algebras, R-matrix.
Alekseevsky, Dmitri and Michor, Peter W. and Ruppert, Wolfgang A.F.
Extension of Lie algebras
Preprint ESI 2000, No. 881
arXiv:math.DG/0005042
Description: A non-super-predecessor of math.QA/0101190
Availability: hardcopy
Extensions of super Lie algebras
J. Lie Theory 15 (2005), no. 1, 125--134
arXiv:math.QA/0101190
Alesker, Semyon
Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables
math.CV/0104209
Alev, J. and Lambre, T.
Comparaison de l'homologie de Hochschild et de l'homologie de Poisson pour une deformation de surfaces de Klein
Algebra and Operator Theory, Kluwer, 1998, 25-38.
Alev, J. and Ooms, M. and van den Bergh, M.
The Gelfand-Kirillov conjecture for Lie algebras of dimension at most eight
J. Alg. 227(2000), 549-581
Description: (Among other), a 6-dimensional Lie algebra sl(2) + Heisenberg and its properties.
Alizade, R. and Pancar, A. and Sezen, B.
Scalar multiplication of proper classes of short exact sequences
Soochow J. Math. 30 (2004), no.2, 127-138
Availability: Scalar.{ps,pdf}
Allen, H.P.
Jordan algebras and Lie algebras of type D_4
circa 1965
Availability: hardcopy
Lie algebras of type D_4 over algebraic number fields
Pacific J. Math. 24, no. 1 (1968), 1-35
Hermitian forms. II
J. Alg. 10(1968), 503-515
Description: Algebras with involution "of type D".
Availability: science-4.pdf
Allen, H.P. and Ferrar, J.C.
New simple Lie algebras of type D_4
BAMS circa 1967
Availability: hardcopy
Jordan algebras and exceptional subalgebras of the exceptional algebra E_6
Pacific J. Math. 32 (1970), N2, 283-297
MR 0262308
Zentralblatt: 0196.06201
Allen, Harry Prince and Sweedler, Moss Eisenberg
A theory of linear descent based upon Hopf algebraic techniques
J. Alg. 12(1969), 242-294
Description: some Hopf-algebraic technique for describing forms; aplications to forms for classical and Witt Lie algebras.
Availability: hardcopy
Allison, Bruce N.
Isomorphism of simple Lie algebras
Trans. Amer. Math. Soc. 177 (1973), 173-190
MR 48#6194
Description: Criteria for central simple Lie algebras over p=0 to be isomorphic.
A construction of Lie algebras from J-ternary algebras
Amer. J. Math. 98 (1976), no.2, 285-294
MR 55#3018
Description: Models of exceptional Lie algebras.
Models of isotropic simple Lie algebras
Comm. Algebra 7 (1979), no.17, 1835-1875
MR 81d:17005
Tensor products of composition algebras, Albert forms and some exceptional simple Lie algebras
DOI: 10.2307/2000817
Trans. Amer. Math. Soc. 306(1988), no.2, 667-695
MR 89e:17004
Isotropic simple Lie algebras of type D_4
Contemp. Math. 110 (1990), 1-21
MR 92b:17009
Construction of 3x3-matrix Lie algebras and some Lie algebras of type D_4
J. Algebra 143 (1991), no.1, 63-92
MR 93b:17069
Lie algebras of type D_4 over number fields
Pacific J. Math. 156 (1992), no.2, 209-250
MR 94c:17017
Zentralblatt: 0785.17006
Description: A full description.
Quartic Cayley algebras and some Lie algebras of type D_4
Proceedings of the International Conference on Algebra, Part 2, Contemp. Math. 131, Part 2, 1992, 15-22
none
Availability: hardcopy (book)
Structurable algebras and the construction of simple Lie algebras
Jordan algebras (Oberwolfach, 1992), 1-8, de Gruyter, Berlin, 1994
MR 95g:17002
Description: Including constructions of some forms of D_4 over number fields.
Availability: hardcopy
Coordinatization of extended affine Lie algebras.
Proceedings of the International Conference on Jordan Structures, Univ. Málaga, 1999, 1-7
none
Allison, Bruce N. and Azam, Saeid and Berman, Stephen and Gao, Yun and Pianzola, Arturo
Extended affine Lie algebras and their root systems.
Mem. Amer. Math. Soc. 126 (1997), 122 pp.
MR 97i:17015
Description: Central extensions of a certain class of Lie algebras.
Availability: hardcopy (book); google books
Allison, Bruce and Benkart, Georgia and Gao, Yun
Central extensions of Lie algebras graded by finite root systems.
DOI: 10.1007/s002080050341
Math. Ann. 316 (2000), no.3, 499-527
MR 2001h:17020
Description: Central extensions of some special class of graded Lie algebras defined over looking like g\otimes A + V\otimes B + D, in terms of dihedral homology of (A + B).
Availability: hardcopy
Lie Algebras Graded by the Root Systems BC_r, r >= 2
Mem. AMS 158 (2002), 158 pp.
Description: Classification, central extensions and invariant forms.
Availability: $32
Allison, Bruce and Berman, Stephen and Faulkner, John and Pianzola, Arturo
Realization of graded-simple algebras as loop algebras
arXiv:math.RA/0511723
Forum Math. 20 (2008), N3, 395-432
Allison, Bruce N. and Berman, Stephen and Gao, Yun and Pianzola, Arturo
A characterization of affine Kac-Moody Lie algebras
Comm. Math. Phys. 185 (1997), no.3, 671-688
MR 98h:17026
Allison, Bruce and Berman, Stephen and Pianzola, Arturo
Covering algebras. I: Extended affine Lie algebras
DOI: 10.1006/jabr.2001.9112
J. Algebra 250 (2002), 485-516
arXiv:math.QA/0103133
Description: Generalization of construction of twisted affine Lie algebras, their automorphisms.
Covering algebras. II. Isomorphism of loop algebras
DOI: 10.1515/crll.2004.044
J. Reine Angew. Math. 571 (2004), 39-71
arXiv:math.QA/0211068
Description: Criteria for isomorphism of some specific twisted loop algebras. Automorphisms, forms.
Availability: hardcopy
Iterated loop algebras
Pacific J. Math. 227 (2006), no. 1, 1--41
arXiv:math.RT/0502225
Description: Strange.
Allison, B.N. and Faulkner, J.R.
The algebra of symmetric octonion tensors
Nova J. Algebra Geom. 2 (1993), no.1, 47-57.
MR 95a:17003
Description: Including forms of E_7
Nonassociative coefficient algebras for Steinberg unitary Lie algebras
J. Algebra 161 (1993), no.1, 1-19.
MR 94j:17004
Availability: av.pdf
Unitary isotopes of structurable algebras
Comm. Algebra 23 (1995), no.4, 1283-1314
MR 96a:17002
Allison, Bruce and Faulkner, John and Yoshii, Yoji
Lie tori of rank 1
Structurable Tori
DOI: 10.1080/00927870801952850
Comm. Algebra 36 (2008), N6, 2265-2332
Allison, Bruce N. and Gao, Yun
Central quotients and coverings of Steinberg unitary Lie algebras
Canad. J. Math. 48 (1996), no.3, 449-482
MR 97f:17022
Description: related to dihedral cohomology
The root system and the core of an extended affine Lie algebra.
DOI: 10.1007/PL00001400
Selecta Math. 7 (2001), no.2, 149-212
MR 1860013
Description: Lie algebras looking like g\otimes A + V\otimes B + D in terms of "coordinate algebra" A+B.
Allison, Bruce and Yoshii, Yoji
Structurable tori and extended affine Lie algebras of type BC1
Journal of Pure and Applied Algebra Volume 184, Issues 2-3 , 1 November 2003, Pages 105-138
Abstract: Structurable n-tori are nonassociative algebras with involution that generalize the quantum n-tori with involution that occur as coordinate structures of extended affine Lie algebras. We show that the core of an extended affine Lie algebra of type BC1 and nullity n is a central extension of the Kantor Lie algebra obtained from a structurable n-torus over . With this result as motivation, we prove general properties of structurable n-tori and show that they divide naturally into three classes. We classify tori in one of the three classes in general, and we classify tori in the other classes when n=2. It turns out that all structurable 2-tori are obtained from hermitian forms over quantum 2-tori with involution.
Allman, Elizabeth S. and Rhodes, John A.
Molecular phylogenetics from an algebraic viewpoint
Statistica Sinica 17 (2007), 1299-1316
Phylogenetic idelas and varieties for the general Markov model
DOI: 10.1016/j.aam.2006.10.002
arXiv:math.AG/0410604
Advances in Applied Mathematics Volume 40, Issue 2, February 2008, Pages 127-148
Availability: hardcopy
Alonso, Juan M. and Hermiller, Susan M.
Homological finite derivation type
Intern. J. Algebra Comput. 13 (2003), No. 3, 341-359
Abstract: In 1987, Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness condition left FP3, and when the monoid is a group, these two properties are equivalent. In this paper we define a new version of finite derivation type, based on homological information, together with an extension of this finite derivation type to higher dimensions, and show connections to homological type FPn for both monoids and groups.
Alpay, Daniel and Schneider, Baruch and Shapiro, Michael and Volok, Dan
Fonctions rationnelles et the'orie de la re'alisation: le cas hyper-analytique
CRAS 336(2003), No.12, 975-980
Zentralblatt: pre01981290
Availability: science.pdf; hardcopy
Alperin, Roger C.
Homology of SL_2(Z[\omega])
Comm. Math. Helv. 55 (1980), N3, 364-377
Free products of matrices
Ulam Quarterly 2 (1993), N2, 1-
Description: Examples of a matrix groups which are free products (generalizing the theme of free subgroups of linear group).
Availability: hardcopy
Alperin, J.L. and Bell, Rowen B.
Groups and Representations
Springer GTM, 1995
Availability: 1995-groups.djvu; google books; Kolkhoz
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Alperin, R.C. and Sahleh, H.
Hopf's formula and the Schur multiplicator for topological groups
Kyungpook Math. J. 31, No.1, 35-71 (1991)
Zentralblatt: 0760.22001
Alperin, Roger C. and Shalen, Peter B.
Linear groups of finite cohomological dimension
Invent. Math. 66 (1982), 89-98
Zentralblatt: 0497.20042
Description: Some interesting reasonings for linear groups over rings.
Availability: alperin.pdf
Al''pin, Yu. A. and Koreshkov, N. A.
On the Simultaneous Triangulability of Matrices
DOI: 10.1023/A:1026659205382
Mathematical Notes Volume 68, Numbers 5-6 / November, 2000 Pages 552-555
Description: A known criterion about simultaneous triangulability of a pair of matrices is deduced from Lie's theorem.
Althoen, S.C. and Hansen, K.D. and Kugler, L.D.
Fused four-dimensional real division algebras
J. Algebra 170(1994), No.2, 649-660
Abstract: Dickson's construction obtains the quaternions as pairs of complex numbers with a specific multiplication. We modify his construction to obtain four-dimensional division algebras from pairs of two-dimensional real division algebras and compare this class of algebras to other known classes.
A survey of four-dimensional C-associative algebras
Algebras Groups Geom. 21(2004), no.1, 9-27
Altinel, Tuna and Borovik, Alexander and Cherlin, Gregory
Simple Groups of Finite Morley Rank
URL: http://math.univ-lyon1.fr/~altinel/ http://www.maths.manchester.ac.uk/~avb/publications.html
AMS, 2008
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Amari, S.I.
Differential Geometrical Methods In Statistics
Lect. Notes Stat., Springer, 1985 (1990?)
Amari, S.I. and Barndorff-Nielsen, O.E. and Kass, R.E. and Lauritzen, S.L. and Rao, C.R.
Differential Geometry in Statistical Inference
Institute of Mathematical Statistics Lecture Note-Monograph Series, Vol. 10, 1987
Amayo, Ralph K.
Lie algebras in which every n-generator subalgebra is an n-step subideal
J. Algebra 31 (1974), 517-542
Zentralblatt: 0285.17006
Lie algebras in which every finitely generated subalgebra is a subideal
Tohoku Math. J. 26 (1974), 1-9
MR 49#2870
Zentralblatt: 0278.17003
A construction for algebras satisfying the maximal condition for subalgebras
Compositio Math. 31 (1975), no.1, 31-46
MR 55#10536
Zentralblatt: 0315.17005
Description: Nonassociative (and particularly Lie) algebras with basis a_i a_j =lambda(i,j) a_{i+j}.
Quasi-ideals of Lie algebras. I, II
DOI: 10.1112/plms/s3-33.1.28
Proc. Lond. Math. Soc. 33 (1976), 28-36 and 37-64
MR 53#13327a and MR 53#13327b
Zentralblatt: 0337.17004 and 0337.17005
Availability: hardcopy
Amayo, Ralph K. and Schwarz, Jochen
Modularity in Lie algebras
Hiroshima Math. J. 10 (1980), no. 2, 311--322
MR 81k:17007
Zentralblatt: 0441.17002
Amayo, Ralph K. and Stewart, Ian
Infinite-dimensional Lie Algebras
Noordhoff, Leyden, 1974, 425 pp.
Description: Various interesting examples: pp.41-, 60-, 72-, 167-; "power series" construction of Hartley: p. 77-; subalgebras of (generalized) Witt algebra: p. 207-209; passing in varieties over field extensions: p.282.
Availability: hardcopy (book); pp. 212-229 are missing and photocopied separately
Amberg, Bernhard and Franciosi, Silvana and Giovanni, Francesco de
Products of groups
Oxford University Press, New York, 1992. xii+220 pp.
MR 94h:20001
Description: Groups representable as product of two subgroups.
Amemiya, Yasuo
What should be done when an estimated between-group covariance matrix is not nonnegative definite?
DOI: 10.2307/2682808
The American Statistician 39 (1985), No. 2, 112-117
Description: Seems to be the same as finding the closest positive-semidefinite matrix.
Availability: 1985-what.pdf; hardcopy
Amemiya, Yasuo and Fuller, Wayne A.
Estimation for the Multivariate Errors-in-Variables Model with Estimated Error Covariance Matrix
URL: http://projecteuclid.org/euclid.aos/1176346502 http://links.jstor.org/sici?sici=0090-5364%28198406%2912%3A2%3C497%3AEFTMEM%3E2%2E0%2ECO%3B2-5
Ann. Statist. Volume 12, Number 2 (1984), 497-509
Description: Something close to estimation of covariance matrix, though in not clear context.
Amenta, N. and Bern, M.
Surface Reconstruction by Voronoi Filtering
Discrete Comput Geom 22:481 504 (1999)
Description: Algorithm for construction of surface encompassing a finite set of points.
Availability: 1999-surface.pdf
Ames, Guillermo and Cagliero, Leandro and Tirao, Paulo
The GL-module structure of the Hochschild homology of truncated tensor algebras
J. Pure Appl. Algebra 193 (2004), no.1-3, 11-26
Zentralblatt: 1060.16007
Description: In terms of Young diagrams.
Amitsur, S.A.
An embeddings of PI-rings
Collected papers, Vol. 1, 301-
Description: Every PI-rings without nilpotent ideals is embedded into: 1. a direct product of central simple algebras whose order over their centers is bounded; 2. total matrix ring over a commutative ring.
Availability: hardcopy (book)
Prime rings having polynomial identities with arbitrary coefficients
PLMS 17 (1967), 470-486
Collected papers, Vol. 1, 417-433
Description: Ultraproducts are employed. An "Amitsur ultrafilter" is constructed (Theorem 3).
Availability: hardcopy (book)
Selected Papers of S.A.Amitsur With Commentary
Parts 1,2, AMS, 2001; hardcover, 583 + 615 pp.
Review: BAMS 40 (2002), N1, 131-135
Availability: hardcopy (books); amazon
Amitsur, S.A. and Rowen, Louis H.
Elements of reduced trace 0
Israel J. Math. 87 (1994), N1-3, 161-179
Zentralblatt: 852.16012
Description: Every element of reduced trace 0 in a simple finite dimensional algebra A is a sum of at most two commutators, and if A is not a division ring, then every non-scalar such element is a commutator.
Availability: book (collection of works of Amitsur)
Ammar, F.
De'formation de l'alge`bre des courants associe'e au groupe de Poincare'
Publ. Math. (U. Autonoma Barcelona) 44 (2000), 193-204
Abstract: Our main purpose in this paper is to compute the second group of local cohomology of the current Lie algebra G_F with type Poincare' Lie group G and stated the local deformations associated.
An, Huihui and Bai, Chengming
From Rota-Baxter Algebras to Pre-Lie Algebras
arXiv:0711.1389
to appear in Journal of Physics A; Mathematical and Theoretical
Description: YBE, Nijenhuis operator, related Lie brackets, etc.
Anan'in, A.Z.
Quasiderivations in diagonal matrix algebras
Third Siberian School Alg. Anal. (ed. L.A.Bokut et al.), AMS Transl. 163 (1995), 1-5
Zentralblatt: 0832.16031
Abstract: Let A be the algebra of all diagonal matrices over a field of characteristic 0. The author shows that 0 is the only quasiderivation of A, and thereby answers a question of Vinberg.
Description: The same, by other methods, was proved by Tevelev (2003).
Availability: p[1,5].png (first and last pages only)
Ancochea-Bermudez, Jose Maria (=Ancochea) and Campoamor-Stursberg, Rutwig (=Campoamor)
Characteristically nilpotent Lie algebras: a survey
Extracta Math. 16 (2001), no. 2, 153-210
arXiv:math.RA/0011224
Availability: hardcopy; liealgebras yahoo group
On Lie algebras whose nilradical is (n-p)-filiform.
Comm. Algebra 29 (2001), no. 1, 427-450
Availability: hardcopy
Classification of (n-5)-filiform Lie algebras.
Linear Algebra Appl. 336 (2001), 167-180
Availability: hardcopy
On certain families of naturally graded Lie algebras
J. Pure Appl. Algebra 170 (2002), no.1, 1-27
Availability: hardcopy; JPPA_170_1.pdf
On a nilpotent Lie superalgebra which generalizes Q_n
Rev. Mat. Complut. 15 (2002), no.1, 131-146
Availability: hardcopy
2-step solvable Lie algebras and weight graphs
DOI: 10.1007/s00031-002-0015-0
Transform. Groups 7 (2002), 307-320
On characteristically nilpotent Lie algebras of type Q
DOI: 10.1016/S0024-3795(02)00618-3
LAA 367 (2003), 193-212
Availability: LAA_367_193.pdf
Some remarks on the classification of graded nilpotent Lie algebras (in Spanish)
Mathematical contributions in honor of Professor Enrique Outerelo Dominguez, 13--19, Homen. Univ. Complut., Editorial Complutense, Madrid, 2004
Description: Filiform.
Availability: Libou2004.pdf
On the cohomology of frobeniusian model Lie algebras
DOI: 10.1515/form.2004.012
Forum Mathematicum 16 (2004), N2, 249-262
Description: Frobenius Lie algebras were classified earlier "up to contractions", and here H^2(L,L) for representatives ("models") is computed.
Ancochea Bermudez, J. M. and Campoamor-Stursberg, Otto Rutwig and Garcia Vergnolle, L.
Les algebres de Lie resolubles rigides reelles ne sont pas necessairement completement resolubles
DOI: 10.1016/j.laa.2006.02.033
Linear Algebra Appl. 418 (2006), no. 2-3, 657--664
Availability: 2006-algebres.pdf
Indecomposable Lie algebras with nontrivial Levi decompositions cannot have filiform radical
Intern. Math. Forum 1 (2006), N7, 309-316
Ancochea Bermúdez, J. M. and Campoamor-Stursberg, R. and García Vergnolle, L. and Goze, M.
Algèbres de Lie résolubles réelles algébriquement rigides
DOI: 10.1007/s00605-007-0467-3
Monatshefte für Mathematik Volume 152, Number 3 / November, 2007 Pages 187-195
Abstract: We present all real solvable algebraically rigid Lie algebras of dimension lower or equal than eight. We point out the differences that distinguish the real and complex classification of solvable rigid Lie algebras.
Ancochea Bermudez, J. M. and Campoamor-Stursberg, R. and Garcia Vergnolle, L. and Sanchez Hernandez, J.
Contractions d'alg\`ebres de Jordan en dimension 2
DOI: 10.1016/j.jalgebra.2008.01.004
arXiv:math.RA/0701477
Journal of Algebra Volume 319, Issue 6, 15 March 2008, Pages 2395-2409
Description: Over real numbers.
Ancochea Bermudez, J. M. and Campoamor-Stursberg, R. and Goze, M. and Garcia Vergnolle, L.
Algebraically rigid real solvable Lie algebras
math.RT/0605300
Description: Classification of dimensiobn <=8 over C and R.
Ancochea Bermudez, J. M. and Fresan, J. and Margalef Bentabol, J.
Contractions of low-dimensional nilpotent Jordan algebras
arXiv:0805.3758
Ancochea Bermudez, J. M. and Fresan, J. and Sanchez Hernandez, J.
On the variety of two dimensional real associative algebras
arXiv:0707.1076
Description: ... decomposing each algebra in A^2 as sum of a Jordan algebra and a Lie algebra...
Ancochea Bermudez, Jose Maria (=Ancochea-Bermudez, Ancochea) and Goze, Michel
Algèbres de Lie rigides
Indag. Math. 88 (1985), 397-415
Zentralblatt: 0577.17008
Description: Using nonstandard analysis. Classification in low dimensions.
Sur la classification des algèbres de Lie nilpotentes de dimension 7
C. R. Acad. Sci Paris 302 (1986), 611-613
Zentralblatt: 0591.17008
Description: Utilizing the so-called characteristic sequence of nilpotent Lie algebras.
Le rang du système linéaire des racines d'une algèbre de Lie rigide résoluble complexe
Comm. Alg. 20 (1992), N3, 875-887
Zentralblatt: 0748.17005
Availability: hardcopy
On the nonrationality of rigid Lie algebras
URL: http://www.ams.org/proc/1999-127-09/S0002-9939-99-04824-8/home.html http://links.jstor.org/sici?sici=0002-9939(199909)127%3A9%3C2611%3AOTNORL%3E2.0.CO%3B2-R
Proc. Amer. Math. Soc. 127 (1999), 2611-2618
Zentralblatt: 1053.17021
On the classification of rigid Lie algebras
DOI: 10.1006/jabr.2001.8880
J. Algebra 245 (2001), N1, 68-91
Zentralblatt: 0998.17010
Availability: Filiform algebras etc.; hardcopy
Ancochea-Bermúdez, José María and Margalef-Bentabol, Juan and Sánchez-Hernández, Jonathan
Sur la Réductibilité des Variétés des Lois d'Algèbres de Leibniz Complexes
Journal of Lie Theory 17 (2007), No. 3, 617--624
Ancochea, J M and Campoamor-Stursberg, R and Garcia Vergnolle, L
Solvable Lie algebras with naturally graded nilradicals and their invariants
J. Phys. A: Math. Gen. 39(2006), 1339-1355
Andaloro, Paul J.
On total stopping times under 3x+1 iteration
Fibonacci Quart. February 2000, 73-78
Zentralblatt: 0949.11007
Availability: hardcopy
The 3x+1 problem and directed graphs
Fibonacci Quart. February 2002, 43-54
Zentralblatt: pre01733247
Availability: hardcopy
Andary, Philippe
Finely homogeneous computations in free Lie algebras
Discr. Math. Theor. Comp. Sci. 1(1997), 101-114
Andersen, H.H. and Jantzen, J.C.
Cohomology of induced reprsentations for algebraic groups
Math. Ann. 269(1984), 487-525
Description: H^* of the first Frobenius kernel with module induced from a Borel subgroup. Koszul resolutions and such. Spectral sequence relating cohomology of G/B (G - algebraic group, B - its Bortel subgroup) with cohomology of the first Frobenius kernel of G.
Availability: aj.pdf
Anderson, Blair M. and Anderson, T. W. and Olkin, Ingram
Maximum Likelihood Estimators and Likelihood Ratio Criteria in Multivariate Components of Variance
URL: http://projecteuclid.org/euclid.aos/1176349929 http://links.jstor.org/sici?sici=0090-5364%28198606%2914%3A2%3C405%3AMLEALR%3E2%2E0%2ECO%3B2-T
Ann. Statist. Volume 14, Number 2 (1986), 405-417
Description: Estimation of covariance matrix in a normal distribution.
Anderson, D. D. and Dumitrescu, Tiberiu
Condensed rings with zero-divisors
Comm. Algebra 33(2005), N11, 3967 - 3976
Description: Conditions like IJ ={ ij | i\in I, j\in j} for ideals I,J.
Availability: g0540j51r298w41j.pdf
Anderson, Ian and Kamran, N.
Conservation laws and the variational bicomplex for second order scalar equations in the plane
Acta Applicanda 41 (1995), 135-144
The variational bicomplex for hyperbolic second-order scalar partial differential equations in the plane
Duke J. Math. 87(1997), 265--319
Description: Some cohomological bicomplex.
Anderson, T. W. and Olkin, I.
Maximum-likelihood estimation of the parameters of a multivariate normal distribution
DOI: : 10.1016/0024-3795(85)90049-7
Lin. Algebra Appl. 70 (1985), 147-171
Description: Exposition on estimation of covariance matrix.
Availability: 1985-maximum.pdf; hardcopy
Anderson, Ian and Pohjanpelto, J.
Infinite dimensional Lie algebra cohomology and the cohomology of invariant Euler-Lagrange complexes: a prelimenary report
Proceedings of the Conference on Differential Geometry and its Applications, Brno, 1995
On the cohomology of invariant variational bicomplexes
Acta Applicanda 41 (1995), 3-19
Anderson, Ian
Introduction to the variational bicomplex
Contemporary Mathematics 132 (1992)
The variational bicomplex
Book draft, Utah, 2004
Availability: web?; Kolkhoz
Anderson, Joel
Commutators of compact operators.
J. Reine Angew. Math. 291 (1977), 128--132
MR 56#1122
Anderson, Robert M.
Non-Standard Analysis with Applications to Economics
in: Handbook of Mathematical Economics, Volume 4, Chapter 39, Elsevier
Anderson, T.W.
Asymptotically efficient estimation of covariance matrices with linear structure
Ann. Stat. 1 (1973), No. 1, 135-141
Availability: 1973-asymptotically.pdf
Maximum likelihood estimation of parameters of autoregressive processes with moving average residuals and other covariance matrices with linear structure
URL: http://projecteuclid.org/euclid.aos/1176343285 http://links.jstor.org/sici?sici=0090-5364%28197511%293%3A6%3C1283%3AMLEOPO%3E2%2E0%2ECO%3B2-2
Ann. Statist. 3 (1975), N6, 1283-1304
Description: Estimation of covariance matrix.
Availability: hardcopy
An Introduction ot Multivariate Statistical Analysis
2nd ed., Wiley, 1984
Availability: 1963-vvedenie.djvu (Russian translation from the 1st ed.)
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Ando, T.
Approximation in trace norm by positive semidefinite matrices
Lin. Algebra Appl. 71(1985), 15-21
Abstract: Information is obtained about best approximation of a matrix by positive semidefinite ones, in trace norm. The situation is much different from approximation in spectral and Euclidean norms.
Availability: ando-positive-semidef.pdf; hardcopy
Ando, Tsuyoshi and Sekiguchi, Takashi and Suzuki, Teruo
Approximation by positive operators
Mathematische Zeitschrift Volume 131, Number 4 December 1973 Pages: 273 - 282
Andrada, Adrian
Hypersymplectic Lie algebras
DOI: 10.1016/j.geomphys.2005.11.006
J. Geom. Phys. 56 (2006), N10, 2039-2067
Description: Complex product structure on Lie algebras and such.
Complex product structures on 6-dimensional nilpotent Lie algebras
Forum Math. 20 (2008), no. 2, 285--315
Description: Related to left-symmetric algebras.
Andrada, A. and Barberis, M. L. and Ovandom, G.
Lie bialgebras of complex type and associated Poisson Lie groups
DOI: 10.1016/j.geomphys.2008.05.006
arXiv:math.DG/0610415
Journal of Geometry and Physics Volume 58, Issue 10, October 2008, Pages 1310-1328
Description: Some (not very complicated) reasonings around complex structures on Lie algebras, YBE, Lie bialgebras, etc. Examples.
Andrada, Adrian and Salamon, Simon
Complex product structures on Lie algebras
arXiv:math.DG/0305102
Forum Math. 17 (2005), no. 2, 261--295
Description: Conditions J[X,Y] = [JX,Y] + [X,JY] + J[JX,JY], and the like. Relation with left-symmetric algebras.
André, Michel
Homologie des algébres commutatives
Springer, 1974
Availability: absent on amazon; Kolkhoz
Andreadakis, Stylianos
On the derivations and automorphisms of Lie algebras
Arch. Math. 17 (1966), 36-43
Zentralblatt: 0236.17006
Availability: hardcopy
On a Lie algebra of polynomials
Bull. Soc. Math. Grece 7 (1966), No.1, 148-153
Zentralblatt: 0149.27805
Description: Some esoteric Lie algebras.
Automorphisms of the polynomial ring k[x] and transformations of the algebraic sets
Bull. Soc. Math. Grece 7 (1966), No.2, 1-49 (in Greek)
Zentralblatt: 0153.50301
Andreev, K.K. and Shabelnikova, D.G.
Characteristic subalgebras of relatively free algebras
DOI: 10.1007/BF00975900
Sib. Mat. J. 14 (1973), N6, 1336-1337
Andrei, Stefan and Kudlek, Manfred and Niculescu, Radu Stefan
Some results on the Collatz problem
Acta Inf. 37(2000), No.2, 145-160
MR 2002c:11022
Zentralblatt: 1003.11005
Availability: AW10YK5GR59L0N1E.pdf; hardcopy
Andrei, Stefan and Masalagiu, Cristian
About the Collatz conjecture
Acta Informatica 35(1998), N2, 167-179
Availability: QX6PXM4JUFN24A5T.pdf; hardcopy
Andreka, Hajnal and Nemeti, Istvan
Los lemma holds in every category
Studia Sci. Math. Hungar. 13 (1978), no. 3-4, 361-376
MR 82i:03049
Description: Not clear.
Availability: hardcopy
Andrews, George E.
The Theory of Partitions
Addison-Wesley, 1976
Availability: Kolkhoz
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Andrews, George E. and Berndt, Brude C.
Ramanujan's Lost Notebook, Part I
Springer, 2005, 437 pp.
Andriyanov, V.I. and Freidman, P.A.
Hamiltonian rings
Sverdlovsk. Gos. Ped. Inst. Uchen. Zap. 31(1965), 3-23
MR 35#5469
Description: description of rings in which every subring is a right ideal.
Andrunakievich, V. A. and Arnautov, V. I. and Goyan, I. M. and Ryabukhin, Yu. M.
Associative rings
DOI: 10.1007/BF01097781
J. Math. Sci. 14 (1980), N1, 922-985
Itogi Nauki i Tekhniki, Alg., Topol., Geom., Vol. 16, VINITI, 1978, 91-190
Zentralblatt: 0405.16001
Description: VINITI survey from RZhMat 1972-1976.
Availability: q10j6806t6331522.pdf
Andrunakievich, V. A. and Arnautov, V. I. and Ryabukhin, Yu. M.
Kolca (in Russian)
Alg., Topol., Geom., 1965, VINITI, 133-
Andrunakievich, V.A. and Ryabukhin, Yu.M.
Radikaly algebr i strukturnaya teoriya
URL: http://techlibrary.ru/books.htm http://orel721.rsl.ru/books_09.06/1/670.djvu
Nauka, 1979 (in Russian)
Availability: absent on amazon; printout of table of content, preface, section 6 of chapter 4, bibliography and index; radikaly.{pdf,djvu}; Kolkhoz
Free commutative quasi-regular algebras and algebras without quasi-regular subalgebras
Rus. Math. Surv. 40 (1985), N4, 147-230
Description: Associative algebras.
Availability: hardcopycopy
Andruskiewitch, Nicolas
On the realization of forms of Kac-Moody algebras
Indag. Mathem. 2(3)(1991), 275-281
MR 93f:17036
Description: constructions of forms of Kac-Moody as current algebras over some rings
Some forms of Kac-Moody algebras.
J. Algebra 147 (1992), no. 2, 324--344.
MR 93j:17048
Andruskiewitch, Nicolas (=Andruskiewitsch) and Jancsa, Patricia
On simple real Lie bialgberas
arXiv:math.QA/0210261
IMRN 2004, N3, 139-158
Abstract: The explicit list of all almost factorizable Lie bialgebra structures on real absolutely simple Lie algebras is given.
Description: Also Manin triples.
Andruskiewitch, Nicolas and Tiraboschi, A.
Lie quasi-bialgebras with quasi-triangular decomposition
J. Lie Theory 10 (2000), 383-397
Description: Some general constructions, going back to Witt.
Angel, Mauricio and Díaza, Rafael
On N-differential graded algebras
DOI: 10.1016/j.jpaa.2006.11.009
Journal of Pure and Applied Algebra Volume 210, Issue 3, September 2007, Pages 673-683
Description: Cohomology associated with d^N = 0.
Anh, P.N. and Marki. L.
Rees matrix rings
J. Alg. 81(1983), N2, 340-369
Description: Matrix rings with multiplication X*Y = XDY for some matrix D.
Anick, D.
On the homology of associative algebras
DOI: 10.2307/2000383
TAMS 296 (1986), N2, 641-659
Description: A minimal free resolution of a trivial module of an associatove algebra is decribed in terms of a Groebner basis of an ideal of relations. Exposition of this result is in Ufnarovskii's VINITI survey.
Annin, B.D. and Bytev, V.O. and Senashov, S.I.
Gruppovye svoistva uravnenii uprugosti i plastichnosti
Nauka, Novosibirsk, 1985 (in Russian)
Availability: Kolkhoz
Apostolov, Vestislav and Armstrong, John and Draghici, Tedi
Local models and integrability of certain almost Kaehler 4-manifolds
DOI: 10.1007/s002080200319
Math. Ann 323 (2002), N4, 633-666
Abstract: We classify, up to a local isometry, all non-Kähler almost Kähler 4-manifolds for which the fundamental 2-form is an eigenform of the Weyl tensor, and whose Ricci tensor is invariant with respect to the almost complex structure. Equivalently, such almost Kähler 4-manifolds satisfy the third curvature condition of A. Gray. We use our local classification to show that, in the compact case, the third curvature condition of Gray is equivalent to the integrability of the corresponding almost complex structure.
Description: Nijenhuis tensor associated with an almost complex structure.
Appel, K. I. and Djorup, F. M.
On the group generated by a free semigroup
DOI: 10.2307/2034609
PAMS 15 (1964), No. 5, 838-840
Description: Group generated by free semigroup is not necessarily free.
Availability: 1964-group.pdf
Applegate, David and Lagarias, Jeffrey C.
Density Bounds for the 3x + 1 Problem. I. Tree-Search Method
Math. Computation 64(1995), No. 209, 411-426.
Availability: density-bounds-1.pdf
Density Bounds for the 3x + 1 Problem. II. Krasikov Inequalities
Math. Computation 64(1995), No. 209, 427-438.
Availability: density-bounds-2krasikov.pdf
The 3x+1 semigroup
math.NT/0411140
J. Number Theory 177 (2006), 147--159
Arad, Z. and Fisman, E. and Muzychuk, M.
Order evaluation of products of subsets in finite groups and its applications
Preprint, January 1995
Availability: hardcopy
Arapura, D.
Complex algebraic varieties and their cohomology
Arbib, Michael A.
Brains, Machines and Mathematics
McGraw-Hill, 1965
Availability: hardcopy
Archibald, R.C.
Mathematicians and music
Amer. Math. Monthly 31(1924), 1-25
Availability: math-music.pdf
Argac, N. and Ponomarev, K. N.
On centroid and extended centroid of rings
Comm. Algebra 31 (2003), no. 6, 3021-3037
Zentralblatt: pre01941731
Availability: centroid.pdf
Arias, Daniel and Ladra, Manuel
Central extensions of precrossed modules
DOI: 10.1023/B:APCS.0000040555.48968.64
Applied Categorical Structures 12 (2004), N4, 339-354
Zentralblatt: 1087.18010
Description: Central extensions are classified via second cohomology.
Ariki, S.
Representations of Quantum Algebras and Combinatorics of Young Tableaux
University Lecture Series, Vol. 26, AMS, 2002 (translation from Japanese, Sophia Univ., 2000); paperback, 158 pp.
Availability: hardcopy
Arhangelskii, A.A.
Completely integrable Hamiltonian systems on a group of triangular matrices
DOI: 10.1070/SM1980v036n01ABEH001778
Math. USSR Sb. 36 (1980), 127-134
Availability: MSB_36_1_A09.pdf
Arkhipov, Sergey
Semi-infinite cohomology of quantum groups
DOI: 10.1007/s002200050170
Comm. Math. Phys. 188 (1997), N2, 379-405
arXiv:q-alg/9601026
Semiinfinite cohomology of associative algebras and bar duality
arXiv:q-alg/9602013, 21 pages
Abstract: Semiinfinite cohomology of associative algebras in terms of Koszul (or bar) duality. Related with the tensor product construction. Semiinfinite cohomology of universal enveloping algebra vs. of Lie algebra.
Semi-infinite cohomology of quantum groups. II
Topics in Quantum Groups and Finite-Type Invariants. Math. at the Indepenedent U. of Moscow (ed. B. Feigin and V. Vassiliev), AMS, 1998
Armstrong, Grant F. and Cairns, Grant and Jessup, Barry
Explicit Betti numbers for a family of nilpotent Lie algebras
Proc. Am. Math. Soc. 125 (1997), No.2, 381-385
Zentralblatt: 0873.17020
Armstrong, Grant F. and Cairns, Grant and Kim, Gunky
Lie algebras of cohomological codimension one
Proc. Amer. Math. Soc. 127 (1999), 709-714.
Zentralblatt: 0966.17016
Abstract: We show that if [$\mathfrak{g}$] is a finite dimensional real Lie algebra, then [$\mathfrak{g}$] has cohomological dimension [$cd(\mathfrak{g})=\dim (\mathfrak{g})-1$] if and only if [$\mathfrak{g}$] is a unimodular extension of the two-dimensional non-Abelian Lie algebra [$\mathfrak{aff}$] .
Availability: S0002-9939-99-04562-1.ps; Cairns' homepage
Arnal, D.
Differential cohomology of C^\infty(G^*)
JGP 4(1987), N4
Description: associative and Lie cohomology and deformations (star-products) of an algebra of C^\infty functions on a dual to an finite-dimensional real Lie algebra.
Availability: hardcopy
Arnal, Didier and Gammella, Angela and Masmoudi, Mohsen
Chevalley cohomology for Kontsevich's graphs
Pacific J.M. 218(2005), N2, 201-239
Availability: hardcopy (journal)
Arnal, D. and Pinczon, G.
On algebraically irreducible representations of the Lie algebra sl(2)
J. Math. Phys. 15 (1974), 350-359
Zentralblatt: 0298.17003
Description: Classification of weighted (inf. dim.) sl(2)-modules.
Arnold, V.I. and Ilyashenko, Yu.S.
Ordinary differential equations
Dynamical Systems I, Encyclopedia of Math. Sci. Vol. 1, Springer, 1-
Description: A VINITI survey.
Availability: ai-ode-viniti.djvu; dynsyst-1.djvu (whole volume); Kolkhoz (Russian edition)
Arnold, B.H.
Logic and Boolean Algebra
Prentice-Hall, 1962; hardcover, dustjacket, 144 pp.
Availability: hardcopy (book)
Arnold, Vladimir I.
One-dimensional cohomologies of Lie algebras of nondivergent vector fields and rotation numbers of dynamic systems
URL: arnold/izbrannoe-60.djvu
Funct. Anal. Appl. 3 (1969), 319-321
Izbrannoe-60, Phasis, 1997, 147-150
Zentralblatt: 0218.58004
On matrices depending on parameters
URL: arnold/izbrannoe-60.djvu
DOI: 10.1070/RM1971v026n02ABEH003827
Russ. Math. Surv. 26 (1971), N2, 29-43
Izbrannoe-60, Phasis, 1997, 155-173
Availability: hardcopy
Lectures on bifurcations in versal families
Russ. Math. Surv. 27 (1972), N4, 54-123
Description: Some interesting reasonings on "deformations" and perturbations of matrices: pp.67-72, but nothing really new compared with the previous paper..
Availability: hardcopy
Spectral sequence for reduction of functions to normal form
Funct. Anal. Appl. 9 (1975), 251-253
Funkts. Anal. Prilozh. 9 (1975), No.3, 81-82
Zentralblatt: 0323.57020
Ordinary Differential Equations
URL: http://techlibrary.ru/books.htm http://ef12517-2.tu-sofia.bg/Desislav Todorov/Frames/Books/Mathematics/differentials equations/
2nd ed., Nauka, 1975 (in Russian); hardcover, 239 pp.
Zentralblatt: 0577.34001
Availability: hardcopy (book); Kolkhoz (4th ed., 2000)
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Spectral sequences for reducing functions to normal forms
Selecta Math. Sovietica 1 (1981), N1, 3-18
Description: Lie algebra of vector fields Der(C[[x_1, ..., x_n]]) considered as a C[[x_1, ..., x_n]]-module (and not vice versa!) Some associated spectral sequence arising from a natural filtration.
Availability: hardcopy
Mathematical Methods of Classical Mechanics
2nd ed., Springer, 1989
Availability: Kolkhoz; google books
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Izbrannoe-60
URL: arnold/izbrannoe-60.djvu
Phasis, Moscow, 1997 (in Russian)
Availability: Kolkhoz
Polymathematics: Is mathematics a single science or a set of arts?
Mathematics: Frontiers and Perspectives (ed. V. Arnold et al.), AMS, 2000, 403-416
Zentralblatt: 0980.00004
Zbl Review: ... all mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA). Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers. Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing. Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry. The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics.
Geometriya kompleksnykh chisel, kvaternionov i spinov
MCCME, 2002 (in Russian)
Gruppy Eulera i arifmetika geometricheskikh progressii
MCCME, 2003 (in Russian)
Availability: Kolkhoz
Mysterious mathematical trinities
Surveys in modern mathematics. The Independent University of Moscow Seminars (ed. V. Prasolov et al.), LMS Lect. Note Ser. 321 (2005), 1-12
Zentralblatt: 1125.00300
Availability: 0521547938_excerpt.pdf (first 10 pages only)
Cepnye drobi (in Russian)
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Vladimir Igorevich Arnol'd (on his 70th birthday)
DOI: 10.1070/RM2007v062n05ABEH004473
Russ. Math. Surv. 62 (2007), 1021-1030
Description: Contains solely Arnold's bibliography after 1997
Availability: rms_62_5_m21.pdf
Arshinov, M.N. and Sadovskii, L.E.
Some lattice-theoretical properties of groups and semi-groups
DOI: 10.1070/RM1972v027n06ABEH001394
Rus. Math. Surv. 27 (1972), N6, 149-191
Description: A survey. Interplay between properties of a group and properties of a lattice of its subgroups.
Availability: VU
Artale, M.
On the resolution of the cokernel of the generic map induced between Schur functors corresponding to a partition
Comm. Alg. 13(1985), 717-744
Description: Resolutions and complexes related to Schur functors and Young diagrams (in Buchsbaum's spirit).
Availability: hardcopy
Artamonov, V.A.
Varieties of restricted Lie algebras
DOI: 10.1007/BF00966552
Sib. Mat. J. 15 (1974), N6, 1197-1212
MR 51#10408
Zentralblatt: 0306.17007
Description: Some special questions of metabelian and abelian varieties of Lie p-algebras. Description of varieties whose lattice of subvarieties forms a chain.
Availability: UVA
On chain varieties of linear algebras
Trans. Amer. Math. Soc. 221 (1976), no.2, 323-338
MR 53#13326
Description: Varieties whose lattice of subvarieties forms a chain.
On finite algebras of prime dimension without subalgebras
DOI: 10.1016/0021-8693(76)90039-9
J. Algebra 42 (1976), no. 1, 247-260.
MR 54#7570
Availability: 1976-finite.pdf; hardcopy
On algebras without proper subalgebras
URL: http://www.iop.org/EJ/abstract/0025-5734/33/3/A05 http://mi.mathnet.ru/msb2948
DOI: 10.1070/SM1977v033n03ABEH002429
Math. USSR Sb. 33 (1977), no.3, 375-401
MR 58#5775485983
Zentralblatt: 0373.17002
Abstract: We study the finite-dimensional algebras over a field that have no proper subalgebras. If the dimension of such an algebra is prime then its automorphism group is a finite cyclic group. Further, under certain hypotheses, algebras of prime dimension having no proper subalgebras and with nontrivial automorphism groups are described.
Availability: MSB_33_3_A05.pdf
Lattices of varieties of linear algebras
DOI: 10.1070/RM1978v033n02ABEH002309
UMN 33 (1978), N2, 135-168; Errata: 34 (1979), no.2, 251
Russ. Math. Surv. 33 (1978), 155-193
MR 81g:08012ab
Zentralblatt: 384.17002
Availability: 1978-lattices.pdf
Universal algebras
DOI: 10.1007/BF01099284
J. Math. Sci. 57 (1991), N2, 2959-3009
Alg. Top. Geom., Vol. 11, VINITI, 191-
Description: A VINITI survey.
Availability: Kolkhoz' obmennik (Russian edition)
Varieties of algebras
Handbook of algebra, Vol. 2, 545-575, North-Holland, 2000
MR 2001e:16035
Availability: vol2.djvu (whole book); hardcopy
Artamonov, V.A. and Salii, V.N. and Skornyakov, L.A. and Shevrin, L.N. and Shulgeifer, E.G.
Obshchaya Algebra
(ed. L.A. Skornyakov), Volume 2, Nauka, Moscow, 1991 (in Russian)
Description: Including an interesting survey chapter on semigroups (by L.N. Shevrin).
Availability: Kolkhoz; absent on amazon; 1991-obshchaya-algebra-2.djvu
Artamonov, V.A. and Slovokhotov, Yu.L.
Gruppy i ikh prilozheniya v fizikie, khimii, kristallografii
Academia, Moscow, 2005
Description: A seemingly pedestrian applicative approach (representations of small Lie groups, etc.).
Availability: 2005-gruppy.djvu
Artemovich, O. D.
Differentiably simple rings: a survey (Ukrainian)
Mat. Stud. 23 (2005), no. 2, 115--128
Artin, E.
Geometric Algebra
URL: http://techlibrary.ru/books.htm http://ef12517-2.tu-sofia.bg/Desislav Todorov/Frames/Books/Mathematics/Algebraic geometry/
5th printing, Interscience Publ., 1966; hardcover, 214 pp.
Availability: hardcopy (book); Kolkhoz (Russian edition)
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Arzhantsev, Ivan V.
Uniqueness of addition in the Lie algebra sl(2)
Vestnik MGU 2000, N4, 49-51
Mosc. Univ. Math. Bull. 55(2000), No.4, 29-31
Lie Algebras, Rings, and Related Topics (ed. Fong Yuen, A.V.Mikhalev and E.Zelmanov), Springer, 2000, 1-4
Zentralblatt: 0984.17005
Description: If L is sl(2) or nonabelian 2-dimensional Lie algebra, and f is a bijection L -> L which preserves multiplication, then f preserves addition.
Availability: reprint-1.ps; hardcopy
Uniqueness of addition in semisimple Lie algebras
Russ. Math. Surv. 56(2001), N3, 569-571
Availability: arzha3u.ps (Russian); reprint-3.ps (English); hardcopy
Some results on uniqueness of addition in Lie algebras
Bajo, Ignacio (ed.) et al., Proceedings of the 1st colloquium on Lie theory and applications, Universidade de Vigo, Vigo, Spain, July 17-22, 2000. Vigo: Universidade de Vigo, Servicio de Publicacio'ns. Colecc. Congr. 35, 19-24 (2002)
Zentralblatt: 1032.17004
Description: Any commutator-preserving bijection on a semisimple Lie algebra or its parabolic subalgebra is additive.
Availability: reprint-4.ps; hardcopy
Arzhantsev, I.V. and Titov, A.V.
Uniqueness of the addition in Lie algebras. I
Vestnik MGU 2001, N2, 59-62
Mosc. Univ. Math. Bull. 56(2001), No.2, 38-40
Zentralblatt: pre01851305
Description: The following condition of Lie algebras over R or C is considered: every continous bijection preserving commutator, also preserves addition. Particularly, all semisimple Lie algebras are such.
Availability: reprint-2.ps; hardcopy
Arzhantseva, G.N.
A property of subgroups of infinite index in a free group
Proc. Amer. Math. Soc. 128 (2000), 3205-3210
Abstract: We prove that if H is a finitely generated subgroup of infinite index in a free group F_m, then, in a certain statistical meaning, the normal subgroup generated by randomly chosen elements r_1, ...r_n of F_m has trivial intersection with H.
Arzhantseva, G.N. and Olshanskii, A.Yu. (=Ol'shanskij)
Generality of the class of groups in which subgroups with a lesser number of generators are free
Math. Notes 59 (1996), no. 3-4, 350-355
Description: In "almost each" group with m generators and n relations, each subgroup generated by less than m elements, is free.
Asashiba, Hideto
Realization of simple Lie algebras via Hall algebras of tame hereditary algebras
J. Math. Soc. Japan 56 (2004), no. 3, 889-905
Domestic canonical algebras and simple Lie algebras
DOI: 10.1007/s00209-007-0246-9
Mathematische Zeitschrift Volume 259, Number 4 / August, 2008 Pages 713-754
Ash, Avner and Gunnells, Paul E. and McConnell, Mark
Cohomology of congruence subgroups of SL_4(Z)
math.NT/0003219
Availability: hardcopy
Ashrafi, Alireza and Venkataraman, Geetha
On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes
Proc. Indian Acad. Sci. 114(2004), N3, 217-224
Description: Generalized quaternion group of order 4n.
Availability: Pm2101.pdf; hardcopy
Aslaksen,
Quaternionic determinants
The Mathematical Intelligencer 18 (1996), no. 3, 56-65
Mathematical Conversation: Selections from The Mathematical Intelligencer", Robin Williams and Jeremy Gray (eds.), 142-156. Springer-Verlag, 2001
97j: MR 16028.
Asmuth, C. and Repka, J.
Tensor products for ${\rm SL}_{2}({\cal K})$. I. Complementary series and the special representation
Pacific J. Math. 97, no. 2 (1981), 271-282
MR 641157
Zentralblatt: 0445.22015
Description: Decomposition of tensor peoducts of two irreducble modules over local fields (?). Some analysis is involved.
Tensor products for ${\rm SL}_{2}({\germ k})$. II. Supercuspidal representations.
Pacific Journal of Mathematics volume 97, issue 1, (1981), pp. 1-18
Assem, Ibrahim and Simson, Daniel and Skowronski, Andrzej
Elements of the Representation Theory of Associative Algebras. Volume 1. Techniques of Representation Theory
Cambridge Univ. Press, 2006
Availability: Kolkhoz; 2006-elements.pdf
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Assmann, B. and Eick, B.
Computing polycyclic presentations for polycyclic rational matrix groups
DOI: 10.1016/j.jsc.2005.05.003
J. Symb. Comput. 40 (2005), N6, 1269-1284
Description: Algorithm for deciding Tits alternative. Implemented in GAP.
Astashkevich, A. B. and Fuchs, D. B.
On the cohomology of the Lie superalgebra W(m|n)
Adv. Sov. M. (AMS) 17(1993), Unconventional Lie Algebras
Availability: hardcopy (book)
Asymptotics for singular vectors in Verma modules over the Virasoro algebra
Pacific J. Math. 177 (1997), no. 2, 201--209.
MR 98e:17034
Astrahan, M. M. and Mehlm J. W. and Putzolu, G. R. and Traiger, I. L. and Wade, B. W. and Watson, V. and Blasgen, M. W. and Chamberlin, D. D. and Eswaran, K. P. and Gray, J. N. and Griffiths, P. P. and King, W. F. and Lorie, R. A. and McJones, P. R.
System R: relational approach to database management
ACM Transactions on Database Systems Volume 1 , Issue 2 (June 1976) Pages: 97 - 137
Description: This is seemingly one of first prototypes of modern relational database systems and SQL.
Availability: p97-astrahan.pdf
Astrakhantsev, V.V.
A characteristic property of simple Lie algebras
Funk. Anal. Pril. 19 (1984), N2, 65-66
Description: p=0. Roots and Cartan decomposition for Lie algebras with nondegenerate symmetric invariant bilinear form, analogous for classical Lie algebras.
Availability: hardcopy
Atabekyan, V.S.
Ob approksimacii v podgruppakh svobodnykh periodicheskikh grupp
Deposited at VINITI, 22.07.1986, N 5380-B86
O prostykh beskonechnykh gruppakh s tozhdestvom
Deposited at VINITI, 22.07.1986, N 5381-B86
Simple and free periodic groups
Vestn. Mosk. Univ., Ser. I 1987, No.6, 76-78
Mosc. Univ. Math. Bull. 42 (1987), No.6, 80-82
MR 89g:20067
Zentralblatt: 0661.20027
Description: Some elucidation of results about monsters. There exists a 2-generated simple group the orders of whose elements are unbounded and which satisfies a nontrivial group law. There exists a continuum of non-isomorphic 2-generated simple torsion-free groups, which satisfies a nontrivial group law, all of whose proper subgroups are cyclic (the latter law may be taken the same as Ol'shanskii's one giving a variety all of whose finite groups are abelian).
Availability: hardcopy
PhD Thesis
Description: Monsters (without torsion and with elements of unbounded exponent) sarisfying a nontrivial identity.
Availability: phd.tar (pp. 65-68 only)
On periodic groups of odd period n >= 1003
DOI: 10.1134/S0001434607090179
Math. Notes 82 (2007), N3-4, 443-447
Description: The set of monsters has continuum cardinality.
Atabekyan, V.S. and Ivanov, S.V.
Dva zamechaniya o gruppakh ogranichennogo perioda
Deposited at VINITI, 30.03.1987, N 2243-B87
Ataguema, Hammimi and Makhlouf, Abdenacer
Deformations of ternary algebras
J. Gen. Lie Theory Appl. 1 (2007), no. 1, 41--55
Athorne, Chris
Hirota derivatives and representation theory
Glasgow Mathematical Journal 43(2001), 1-8
Abstract: It is shown that the Hirota derivative can be used to construct the plethysm for tensor products of representations of {sl}_2(k).
Atiyah, M.F.
K-Theory
Mir, 1967 (Russian translation entitled "Lekcii po K-teorii")
Availability: Kolkhoz
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Atiyah, M. F. and Bott, R.
A Lefschetz fixed point formula for elliptic complexes. I
Ann. Math. 86(1967), No.2, 374-407
Description: Euler-Poincare char.
Availability: lefschetz-1.pdf
A Lefschetz fixed point formula for elliptic complexes. II
Ann Math. 88(1968), 451-491
Atiyah, M.F. and Macdonald, I.G.
Introduction to Commutative Algebra
Mir, 1972 (Russian translation from Addison-Wesley, 1969); paperback, 160 pp.
Availability: Kolkhoz (Addison-Wesley, 1969); hardcopy (book)
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Atiyah, M.F. and Shapiro, A.
Clifford modules
Availability: clifford-modules.djvu
Atiyah, M. and Wall, C (?)
Kogomologii grupp
Algebraic Number Theory (ed. J.W.S.Cassels and A.Frohlich), Acad. Press, 1967, 150-
Description: A very nice, short and useful introduction to group (co)homology.
Availability: Kolkhoz (Russian translation, 1969)
Atsuyama, Kenji
Another construction of real simple Lie algebras
Kodai Math. J. 6, no. 1 (1983), 122-133
Attiogbe, Cyril Efoe
On characterizing nilpotent Lie algebras by their multipliers
URL: http://wwwlib.umi.com/dissertations/fullcit/3128736 http://www.lib.ncsu.edu/theses/available/etd-03272004-213159/unrestricted/etd.pdf
PhD Thesis, North Carolina State Univ., 2004, 77 pages.
Aubry, Gregoire
Algebraic approach to population genetic
Ecole Polytechn. Fed. Losanne, 2004, 41 pp.
Description: At chapter 6, probably some useful examples of algebaric structures significance.
Availability: Algebraic_approach_to_population_genetics-Gregire_Aubry.pdf; web
Audin, Michele
Lectures on gauge theory and integrable systems
Gauge Theory and Symplectic Geometry (ed. J. Hurtubise and F. Lalonde), Kluwer, 1997, 1-48
Availability: 1997-lectures.djvu
Spinning Tops
Cambridge Univ. Press, 1999; paperback, 139 pp.
Availability: hardcopy (book)
Publier sous l'Occupation I. Autour du cas de Jacques Feldbau et de l'Académie des sciences
arXiv:0711.0447
Availability: hardcopy (arXiv version 1)
Ault, Shaun and Fiedorowicz, Zbigniew
Symmetric Homology of Algebras
arXiv:0708.1575
Description: An analog of cyclic homology, where the cyclic group is replaced by symmetric group.
Auslander, L. and Brezin, J.
Almost algebraic Lie algebras
DOI: