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Eakin, Paul and Sathaye, Avinash
On automorphisms and derivations of Cayley-Dickson algebras
J. Algebra 129, No.2, 263-278 (1990)
MR 91b:17002
Zentralblatt: 0699.17022
Easson, Vivien R.
Groups of cohomological dimension less than or equal to 2
Cambridge U. Part III course essay, May 2001, 33p.
Description: a survey
Availability: cohdim.ps
Eastwood, Michael
Variations on the de Rham Complex
Notices AMS, December 1999
Eaton, M.L.
Multivariate Statistics: A Vector Space Approach
Wiley, 1983
Inst. Math. Stat., 2007
MR 0716321
Zentralblatt: 0587.62097
Ebbinghaus, Heinz-Dieter and Flum, Jörg
Finite Model Theory
DOI: 10.1007/3-540-28788-4
2nd ed., Springer, 2006
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Eberly, W. and Giesbrecht, M.
Efficient decompositon of associative algebras
Proc. ISSAC'86, 170-178
Description: Algorithms for finding Wedderburn decomposition.
Availability: hardcopy
Efficient decomposition of separable algebras
DOI: 10.1016/S0747-7171(03)00071-3
J. Symbolic Comput. 37 (2004), N1, 35-81
Description: Probabilistic algorithm for finding generator of the center of finite-dimensional associative algebra.
Ebrahimi-Fard, K. and Guo, L. and Manchon, D.
Birkhoff type decompositions and the Baker-Campbell-Hausdorff recursion
DOI: 10.1007/s00220-006-0080-7
arXiv:math-ph/0602004
Comm. Math. Phys. 267 (2006), N3, 821-845
Description: Play with BCH formula in context of filtered and graded algebras.
Availability: hardcopy; fulltext.pdf (journal article)
Echarte, F.J. and Nunez, J. and Ordonez, M.
Derived filiform Lie algebras having first coefficient 0
Analele Univ. Bucuresti. Mat. 49(2000), N2, 141-154
Zentralblatt: (me)
Availability: hardcopy
Eckmann, Beno
Mathematical Miniatures
Preprint Forschungsinst. fuer Math., ETH Zuerich, 2005, 58 pp.
Description: Very diverse and largely intersting essays: history of homological algebra, history of ETH, continuity vs. linearity, etc.
Hermann Weyl in Zurich 1950-1955
Notices AMS, 2006
Eckmann, Beno and Hilton, Peter and Stammbach, Urs
On the homology theory of central group extensions. I. The commutator map and stem extensions
DOI: 10.1007/BF02566792
Comment. Math. Helv. 47 (1972), 102--122
MR 47#357
Zentralblatt: 0236.20038
On the homology theory of central group extensions. II. The exact sequence in the general case
Comment. Math. Helv. 47 (1972), 171--178; Corrigendum: 48(1973), 136
MR 47#8699
Zentralblatt: 0246.20041
Eckmann, Beno and Stammbach, Urs
On exact sequences in the homology of groups and algebras
Ill. J. Math. 14, 205-215 (1970)
Zentralblatt: 0195.03402
Description: Homology in degree 1,2, including Lie algebras.
Edelman, Alan and Elmroth, Erik and Kagstrom, Bo
A geometric approach to perturbation theory of matrices and matrix pencils. Part I: Versal deformations
DOI: 10.1137/S0895479895284634
SIAM J. Matrix Anal. Appl. 18 (1997), No. 3, 653-692
Description: Arnold-like theory for versal deformations of matrix pencils.
Availability: hardcopy
Edelsbrunner, H. and Harer, J.
Persistent homology --- a survey
Twenty Years After, eds. J. E. Goodman, J. Pach and R. Pollack, AMS, to appear
Edmundo, Mario J.
Solvable groups definable in o-minimal structures
math.LO/0012041, 43 pages, submitted
Abstract: Let N be an o-minimal structure. In this paper we develop group extension and group cohomology theory over N and use it to describe the N-definable solvable groups. We prove an o-minimal analogue of the Lie-Kolchin-Mal'cev theorem and we describe the N-definable G-modules and the N-definable rings.
Efron, B.
Netradicionnye metody mnogomernogo statisticheskogo analiza
Finasy i statistika, Moscow, 1988
Description: Collection of papers.
Availability: 1988-netradic.djvu
Efthimiou, C. J. and Spector, D. A.
A Collection of Exercises in Two-Dimensional Physics, Part 1
hep-th/0003190
Description: This is however not the "real" two-dimensional physics (or rather mechanics) I wish to expect. It jumps directly to path integral and devoted exclusively to such abstract nonsense as CFT.
Egorov, George
How to superize gl(\infty)
Diff. Geom. Meth. Math. Phys. (J.Mickelsson, O.Peckonnen, eds.), World Sci., 1992, 135-146
Zentralblatt: pre01467405
Availability: gl-infty.{tex,dvi}
Egorychev, G.P.
Integral Representation and the Computation of the Combinatorial Sums
URL: http://techlibrary.ru/books.htm http://orel721.rsl.ru/books_09.06/1/739.djvu
AMS, 1984
Availability: comb-sums.{pdf,djvu}; amazon; Kolkhoz
Eguchi, Tohru and Gilkey, Peter B. and Hanson, Andrew J.
Gravitation, gauge theories and differential geometry
Physics Reports 66(1980), N6, 213-393
Description: Seems to be a pleasant intro to such topics as fibre bundles, (co)homology of manifolds, characteristic classes, etc.
Availability: diff.pdf
Eick, Bettina
Computing the automorphism group of a solvable Lie algebra
DOI: 10.1016/j.laa.2003.12.009
Linear Algebra Appl. 382, 195-209 (2004)
Zentralblatt: 1045.17001
Description: Including algorithm for computing second cohomology group of a solvable algebra.
Eick, Bettina and Niemeyer, Alice C. and Panaia, Oreste
A polycyclic quotient algorithm
Research report 2003/18, The U. of Western Australia
Abstract: We describe an algorithm to compute polycyclic presentations for (possibly infinite) polycyclic quotients of finitely presented groups.
Availability: hardcopy
Eidelkind, D. I.
Exact representations for free groups
DOI: 10.1007/BF02219814
Algebra and Logic 10 (1971), N4, 281-296
Description: A few-lines proof of the Platonov's theorem on linear groups with identities.
Availability: 1971-exact.pdf
Eilenberg, Samuel
Algebras of cohomologically finite dimension
Comment. Math. Helv. 28 (1954), 310-319
Description: Finite-dimensional associative algebras such that all cohomology up to certain degree vanishes, are separable.
Availability: algebras.pdf
Eilenberg, Samuel and MacLane, Saunders
Cohomology theory in abstract groups. I
Ann. Math. 48 (1947), No.1, 51-78
Zentralblatt: 0029.34001
Availability: ce.pdf
Cohomology theory in abstract groups. II: Group extensions with a non-abelian kernel
DOI: 10.2307/1969174
Ann. Math. 48 (1947), No.2, 326-341
Eilenberg, S. and Rosenberg, A. and Zelinsky, D.
On the dimension of modules and algebras. VIII. Dimension of tensor products
Nagoya Math. J. 10 (1957), 71-93
MR 0098774
Zentralblatt: 0212.05901
Availability: 1957-dimension.pdf
Eilenberg, Samuel and Schutzenberger, M. P.
On pseudovarieties
DOI: 10.1016/0001-8708(76)90029-3
Adv. Math. 19 (1976), no.3, 413-418
MR 53#5431
Description: Classes of finite universal algberas clsoed under finite direct products, etc.
Availability: science.pdf; hardcopy
Einstein, A.
Ideas and Opinions
Bonanza Books, New York, 1954; hardcover with dustjacket, 377 pp.
Availability: hardcopy (book)
Eisenbud, David
Commutative Algebra with a View Toward Algebraic Geometry
DOI: 10.1090/S0273-0979-96-00662-3
Springer, 1995
Review: Bull. Amer. Math. Soc. 33 (1996), 367-370
Description: Groebner bases, Koszul complex.
Availability: commalg.djvu; Kolkhoz; google books
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Periodic resolutions over exterior algebras
Special issue in celebration of Claudio Procesi's 60th birthday. J. Algebra 258 (2002), no. 1, 348--361
Eisenbud, D. and Harris, J.
Vector spaces of matrices of low rank
Adv. Math. 70(1988), 135-155
Eisenbud, David and Weyman, Jerzy
Fitting's lemma for Z/2-graded modules
math.AG/0202227
TAMS June 10, 2002
Description: A superanalogue of Cauchy formula for S^*(U \otimes V).
Availability: S0002-9947-03-03198-2.ps (published paper)
Ekdiha, M. and El galiou, M.
Cohomologie de certains bi-complexes et applications aux structures de Poisson
DOI: 10.1081/AGB-200034012
Comm. Algebra 33 (2005), no. 1, 1--17
Availability: WQQ44434327J747J.pdf
Ekeland, I.
Exterior Differential Calculus and Applications to Economic Theory
Scuola Normale Superiore, Edizione Della Normale, 1998
Availability: 18 EUR
Eklof, P.
Ultraproducts for algebraists
Handbook of Math. Logic, N.-Holland, 1977, 105-137
Availability: hardcopy; vol1.djvu (the whole book, in Russian)
El Agawany, M. and Micali, A.
Le theoreme de Poincare-Birkhoff-Witt pour les algebre de Lie graduee
CRAS 285 (1977), N4, 165-168
Superalgebres de Lie et le theoreme de Poincare-Birkhoff-Witt
Algebras Groups Geom. 4 (1987), 1-44
Zentralblatt: 0633.17002
Description: Seems to be a superization of Sridharan results (Lie algebras with cocycles leading to PBW-algebras)
El-Amin, Kaidi and Isabel Rami'rez, Maria and Rodri'guez Palacios, Angel
Absolute-Valued Algebraic Algebras Are Finite-Dimensional
Journal of Algebra Volume 195, Issue 1 , 1 September 1997, Pages 295-307
Abstract: If A is a non-associative algebra over R, if there is a norm on A satisfying ||xy|| = ||x|| ||y||, and if every one-generated subalgebra of A is finite-dimensional, then A is finite-dimensional.
El Houari, Mohammed
Tensor invariants associated with classical simple Lie algebras: illustration of a new classiciation of simple Lie algebas
ICTP Preprint No.IC96245, 1996
Description: Around some new classification of simple Lie algebras over C.
Immediate applications of a new classification of finite dimensional simple Lie algebras
Nonassociative Algebra and Its Applications (ed. R.Costa, A.Grishkov), M.Dekker, 2000, 55-
Availability: classif.tar (selected pages only)
google books
El Khamlichi, L. and Haddi, A.
On braided homology
Cahen, Paul-Jean (ed.) et al., Commutative ring theory. Proceedings of the 2nd international conference, Fe`s, Morocco, June 5--10, 1995. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 185, 283-292 (1997)
Zentralblatt: 0867.18006
Description: Previous Haddi's considerations about homology of current algebras in the context of braided category.
El Kinani, E. H.
Between quantum Virasoro algebra $\scr L_c$ and generalized Clifford algebras
Adv. Appl. Clifford Algebras 13 (2003), no. 2, 127--132
El Malek, Alfy Abd (= Malek) and Micali, Artibano
Algebres de Malcev faiblement restreintes
Algebras Groups Geom. 3(1986), 414-430
Zentralblatt: 0617.17011
Description: Schue's 1969 results about Cartan decompositions in Lie algebras for Malcev algebras.
Availability: hardcopy
Elashvili, A.G. (=Ehlashvili)
Plasty prostykh algebr Lie osobogo tipa
typewritten manuscript
Availability: hardcopy
Centralizatory nilpotentnykh elementov v poluprostykh algebrakh Lie
Trudy Tbilis. Mat. Inst. 46 (1975), 109-132
Availability: hardcopy
Frobenius Lie algebras
DOI: 10.1007/BF01077870
Funct. Anal. Appl. 16 (1983), 326-328
Zentralblatt: 0519.17005
Description: A Lie algebra L is called Frobenius, if there is a linear form L->K such that the bilinear form f([x,y]) is nondegenerate.
Availability: hardcopy
Frobenius Lie algebras. II (in Russian)
Trudy Tbilis. Mat. Inst. Razmadze 77 (1985), 127-137
Zentralblatt: 0626.17007
Description: Also Lie algebras having a nondegenerate 2-cocycle.
Elashvili, A.G. and Kac, V.G.
Classification of good gradings of simple Lie algebras
arXiv:math-ph/0312030 (under different title)
Lie Groups and Invariant Theory, AMS Transl. 213 (2005), 85-
Description: Z-gradings of simple finite-dimensional Lie algebras.
Availability: hardcopy (arXiv version); google books
Elashvili, Alexander G. and Ooms, Alfons I.
On commutative polarizations
DOI: 10.1016/S0021-8693(03)00146-7
arXiv:math.RT/0302229
J. Algebra 264 (2003), No.1, 129-154
Zentralblatt: 1035.17010
Description: P - subalgebra in L (p=0, alg. cl.) is called polarization if P is maximal totally isotropic subspace with respect to some linear form f:L->K.
Elduque, Alberto
A note on noncentral simple minimal nonabelian Lie algebras
DOI: 10.1080/00927878708823472
Comm. Alg. 15 (1986), N7, 1313-1318
Availability: hardcopy
On Lie algebras with a subalgebra of codimension 1
DOI: 10.1007/BFb0088887
LNM 1373 (1989), 1-28
Description: Related to forms of W_1(n), p>2.
Availability: 1989-lie.pdf
On semisimple Malcev algebras
DOI: 10.2307/2048037
Proc. AMS 107 (1989), No. 1, 73-82
Description: Decomposition of semisimple Maclev algebras into the direct sum of "Lie" and "non-Lie" parts. Block's theorem on differentiable simple rings is employed.
Availability: 1989-semisimple.pdf
A note on modules for noncentral simple Lie algebras
DOI: 10.1080/00927879108824180
Comm. Alg. 19 (1991), 945-949
Description: When a module over a simple Lie algebra over nonalgebraically-closed field carries a structure of a module over the same Lie algebra over centroid.
Availability: hardcopy
Okubo algebras and twisted polynomials
Recent Progress in Algebra, Contemp. Math. 224 (1999), 101-109
Description: Algebra structures defined on sl(n+1) of the form x*y = axy + byx - (a+b)/(n+1) Tr(xy) E.
Availability: Google books; 1999-okubo.tar
Symmetric composition algebras
DOI: 10.1006/jabr.1997.7071
J. Algebra 196 (1997), N1, 283-300
Description: Equivalent constrcutions of Okubo algebras, see above.
Quaternions, octonions and the forms of the exceptional simple classical Lie superalgebras
URL: http://mathematik.uibk.ac.at/mathematik/jordan/archive/quaoclie/index.html http://www.springerlink.com/openurl.asp?genre=article&issn=0010-2571&volume=79&issue=1&spage=208
Comment. Math. Helv. 79 (2004), no.1, 208-228
The magic square and symmetric compositions
URL: http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.rmi/1087482023 http://dmle.cindoc.csic.es/en/revistas/detalle.php?numero=2029 http://www1-c703.uibk.ac.at/mathematik/jordan/archive/magic/magic.pdf
Rev. Mat. Iberoamericana 20 (2004), no.2, 475-491
MR 2073128
Zentralblatt: pre02110195
Symmetric composition algebras and Freudenthal's magic square
Resenhas 6 (2004), no.2-3, 165--176
New simple Lie superalgebras in characteristic 3
DOI: 10.1016/j.jalgebra.2005.06.014
J. Algebra 296 (2006), N1, 196-233
arXiv:math.RA/0412395
Description: Also new models of some nonclassical simple Lie algebras.
A new look at Freudenthal's magic square
Non-associative algebra and its applications, 149--165, Lect. Notes Pure Appl. Math., 246, Chapman & Hall/CRC, 2006
A Lie grading which is not a semigroup grading
DOI: 10.1016/j.laa.2006.02.006
Lin. Alg. Appl. 418 (2006), N1, 312-314
The magic square and symmetric compositions. II
Rev. Mat. Iberoamericana 23 (2007), no. 1, 57--84
arXiv:math.RT/0507282
Abstract: ... all the Lie algebras in Freudenthal's Magic Square can be constructed, in a unified way, using copies of sl(2) and of its natural module.
Some new simple modular Lie superalgebras
Pacific J. Math. 231 (2007), no. 2, 337--359
arXiv:math.RA/0512654
Description: p=3,5, Tits construction.
The Tits construction and some simple Lie superalgebras in characteristic 3
J. Lie Theory 18 (2008), No.3, 601--615
arXiv:math.RA/0703784
Abstract: Some simple Lie superalgebras, specific of characteristic 3, defined by Bouarroudj and Leites, are shown to be related to the simple alternative and commutative superalgebras discovered by I.P. Shestakov.
Models of some simple modular Lie superalgebras
arXiv:0805.1304
Gradings on symmetric composition algebras
arXiv:0809.1922
Description: Also gradings of exceptional Lie algebras.
More non semigroup Lie gradings
arXiv:0809.4547
Description: More examples of Lie algebras with grading which is not a semigroup grading.
Elduque, A. and Gonzalez, S. and Martinez, C.
Unit element in mutation algebras
Algebras Groups Geom. 1(1984), 386-398
Elduque, Alberto and Labra, Alicia
On the classification of commutative right-nilalgebras of dimension at most four
DOI: 10.1080/00927870601074780
Comm. Algebra 35 (2007), N2, 577 - 588
Pre-publ. Sem. Mat. "Garcia de Galdeano" 2007, N8
On the Classification of Commutative Right-Nilalgebras of Nilindex 5 and Dimension 4
DOI: 10.1080/00927870801937380
Communications in Algebra, Volume 36, Issue 5 May 2008 , pages 1704 - 1716
Elduque, Alberto and Laliena, Jesús and Sacristán, Sara
Maximal subalgebras of associative superalgebras
DOI: 10.1016/j.jalgebra.2003.12.018
J. Algebra 275 (2004), N1, 40-58
Abstract: Non-super case, including of algebars with involution, is also treated.
Maximal subalgebras of Jordan superalgebras
DOI: 10.1016/j.jpaa.2008.03.012
Journal of Pure and Applied Algebra Volume 212, Issue 11, November 2008, Pages 2461-2478
Description: Over an algebraically closed field.
Elduque, A. and Montaner, F.
On mutations of associative algebras
J. Korean Math. Soc. 28(1991), 143-156
Description: x*y = xpy - yqx
Availability: hardcopy; kqe87pgp.dvi
A note on derivations of simple algebras
J. Alg. 165(1994), No.3, 636-644
Abstract: Necessary and sufficient conditions for all the derivations of a finite dimensional simple nonassociative algebra, over a field of characteristic zero, to be inner are given in terms of the Lie multiplication algebra and trace of the derivations.
Availability: sdarticle.pdf
Elduque, Alberto and Montaner, Fernando and Myung, Hyo Chul
Automorphisms and derivations in a class of Jordan and Malcev admissible algebras
Nova J. Algebra Geom. 2, No.1, 1-45 (1993)
Zentralblatt: 0871.17030
Description: (among all), criteria for two mutations (of two algebras) to be isomorphic
Elduque, Alberto and Myung, Hyo Chul
On mutations of Cayley-Dickson algebras
Second international conference on algebra dedicated to the memory of A. I. Shirshov (ed. L.A. Bokut et al.), Contemp. Math. 184 (1995), 97-110
Zentralblatt: 0837.17018
Availability: hardcopy (book)
Color algebras and affine connections on S_6
J. Algebra 149 (1992), No.1, 234-261
Zentralblatt: 0773.17001
Description: Some interesting nonassociative algebras arising from Cayley-Dickson algebras (by taking projection of multiplication on subspaces, etc.).
Availability: 1992-colour.pdf
Mutations of alternative algebras
Kluwer, 1994, 226pp.
Review: Bull. Amer. Math. Soc. 33 (1996), 227-228
Description: A mutation of an algebra A is a new algebra defined on A with multiplication [x,y] = xay - ybx for some fixed a,b in A.
Availability: TUDelft: TW - 17D05 Eldu; absent in Iceland, UVA, VU and CWI; 1994-mutations/ (page 214 only); google books
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Colour algebras and Cayley-Dickson algebras
Proc. R. Soc. Edinb. Sect. A 125 (1995), No.6, 1287-1303
Zentralblatt: 0855.17001
Description: Some interesting nonassociative algebras arising from Cayley-Dickson algebras (by taking projection of multiplication on subspaces, etc.).
Octonions and affine connections on spheres
Nonassociative Algebra and Its Applications (ed. R.Costa and A.Grishkov), M.Dekker, 2000, 43-
Availability: octonions.tar (few pages only)
google books
Elduque, Alberto and Okubo, Susumu
Composition superalgebras
Comm. Algebra 30 (2002), no. 11, 5447-5471
Zentralblatt: 1015.17002
Abstract: The super counterparts of both unital composition algebras and of symmetric composition algebras are classified. It turns out that new objects arise only over fields of characteristic 3. The Principle of Local Triality is considered for this new objects. It is related to some order 3 automorphisms of the simple Lie superalgebras osp(1,2) and osp(4,2) in characteristic 3.
Lie algebras with S4-action and structurable algebras
DOI: 10.1016/j.jalgebra.2006.08.033
J. Algebra 307 (2007), N2, 864-890
arXiv:math.RA/0508558
S4-symmetry on the Tits construction of exceptional Lie algebras and superalgebras
Publicacions Matematiques 52 (2008), N2, 315-346
arXiv:math.RA/0611303
Lie algebras with S3 or S4-action, and generalized Malcev algebras
arXiv:0801.2481
Elduque, A. and Varea, V. R.
Lie algebras all of whose subalgebras are supersolvable
Lie algebras and related topics, Canad.~Math.~Soc.~Conf.~Proc. \textbf{5} (1986)
Elduque, Alberto and Villa, Oliver
The existence of superinvolutions
arXiv:0704.3127
Journal of Algebra Volume 319, Issue 10, 15 May 2008, Pages 4338-4359
Description: Superinvolutions of the first and second kind in associative superalgebras.
Elek, Gabor and Samet-Vaillant, Aryeh
The ends of algebras
math.RA/0504227
Comm. Algebra 34 (2006), N8, 2967 - 2975
Elgueta, Josep
Cohomology and deformation theory of monoidal 2-categories I
arXiv:math.QA/0204099
Abstract: We define a cohomology for an arbitrary $K$-linear semistrict semigroupal 2-category $(\mathfrak{C},\otimes)$ (called in the paper a Gray semigroup) and show that its first order (unitary) deformations, up to the suitable notion of equivalence, are in one-one correspondence with the elements of the second cohomology group. Fundamental to the construction is a double complex, similar to Gerstenhaber-Schack's double complex for bialgebras. We also identify the cohomologies describing separately the deformations of the tensor product, the associator and the pentagonator. To obtain these results, a cohomology theory for an arbitrary $K$-linear unitary pseudofunctor is introduced describing its purely pseudofunctorial deformations, and generalizing Yetter's cohomology for semigroupal functors. The corresponding higher order obstructions will be considered in a future paper.
Elizarov, V.P.
Strong pretorsion and strong filters, modules and rings of fractions
Sib. M. J. 14 (1973), 380-387
Description: Related to the ultraproduct construction.
Elkies, Noam D. and Gross, Benedict H.
Cubic rings and the exceptional Jordan algebra
Duke Math. J. 109 (2001), no. 2, 383-409
Ellis, Graham J.
Non-abelian exterior product of Lie algebras and an exact sequence in the homology of Lie algebras
DOI: 10.1016/0022-4049(87)90088-0
J. Pure Appl. Alg. 46 (1987), 111-115
MR 88k:17016
Description: 6-term exact sequence (over commutative ring) generalizing the 5-term one arising from the Hochschild-Serre spectral sequence.
Availability: science.pdf
A non-abelian tensor product of Lie algebras
Glasgow Math. J. 33 (1991), 101-120
MR 92g:18010
Homotopical aspects of Lie algebras
J. Austral. Math. Soc. 54 (1993), 393-415
Description: Mayer-Vietoris long exact sequence and other goodies for simplicial Lie algebras. Hint that Mayer-Vietoris sequences and (different variants of) exact sequence relating in a Hopf-like manner low-dimensional homology of L/I, L/J and L/(I+J) have the same (simplicial?) origin.
Availability: ellis.ps (very non-optimized ps); hardcopy
The Schur multiplier of a pair of groups
DOI: 10.1023/A:1008652316165
Appl. Categor. Struct. 6 (1998), N3, 355-371
Computing group resolutions
DOI: 10.1016/j.jsc.2004.03.003
J. Symb. Comput. 38 (2004), N3, 1077-1118
Description: For groups given by presentation, in GAP, using syzigies.
Homological algebra programming
Computational Group Theory and the Theory of Groups, Contemp. Math. 470 (2008)
Ellis, Graham and Kholodna, Irina
Computing second cohomology of finite groups with trivial coefficients
Homology, Homotopy and Appl. 1 (1999), 163-168
Description: Via presentation; procedure for computing in Magma.
Availability: hardcopy
Elsting, G.O.
Systems of generators in certain simple Lie algebras
Izv. VUZ 19(1975), N4, 112-115
Description: p>0. For classical Lie algebras, for any x there is y such that x,y generate the whole algebra. Lie algebras of Cartan type are 2-generated.
Availability: hardcopy
GRADED LIE ALGEBRAS WITH LONG GRADINGS
DOI: 10.1070/RM1979v034n02ABEH002917
RUSS MATH SURV, 1979, 34 (2), 223-224
On analogs of classical Lie algebras over a field of characteristic 3
Soviet Math. (Izv. VUZ) 35(1991), N7, 61-65
Availability: UVA
Emmanouil, Ioannis and Mikhailov, Roman
A limit approach to group homology
DOI: 10.1016/j.jalgebra.2007.12.006
Journal of Algebra Volume 319, Issue 4, 15 February 2008, Pages 1450-1461
Description: H_2n(G,Z) = limit of H_0(G,tensor module of relations).
Emmanouil, Ioannis and Passi, Inder Bir S.
Group homology and Connes' periodicity operator
DOI: 10.1016/j.jpaa.2005.07.008
J. Pure Appl. Algebra 205 (2006), N2, 375-392
Description: Related to cyclic homology of group rings.
Group homology and extensions of groups
Homology, Homotopy and Applications, Vol. 10 (2008), No. 1, pp.237-257.
Abstract: Using Quillen's description of cyclic cohomology in terms of traces on algebra extensions and Burghelea's computation of the cyclic homology of the group algebra of a group Pi, we derive a description of the homology of Pi with coefficients in a field of characteristic 0 as the inverse limit of a functor on the category of extensions of Pi.
Enright, Thomas J. and Hunziker, Markus
Resolutions and Hilbert series of determinantal varieties and unitary highest weight modules
J. Algebra 273 (2004), no. 2, 608--639
Enright, Thomas J. and Hunziker, Markus and Wallach, Nolan R.
A Pieri rule for Hermitian symmetric pairs I
Abstract: Let $(G,K)$ be a Hermitian symmetric pair and let $\g$ and $\k$ denote the corresponding complexified Lie algebras. Let $\g=\k \oplus \p^+\oplus \p^-$ be the usual decomposition of $\g$ as a $\k$-module. $K$ acts on the symmetric algebra $S(\p^-)$. We determine the $K$-structure of all $K$-stable ideals of the algebra. Our results resemble the Pieri rule for Young diagrams. The result implies a branching rule for a class of finite dimensional representations that appear in the work of Enright and Willenbring (preprint, 2001) and Enright and Hunziker (preprint, 2002) on Hilbert series for unitarizable highest weight modules.
Enriquez, B.
On some universal algebras associated to the category of Lie bialgebras.
Adv. Math. 164 (2001), no. 1, 1-23
math.QA/0101059
A cohomological construction of quantization functors of Lie bialgebras
Preprint IRMA 2003-003
Description: Schur functors are involved.
Entov, Michael
Commutator length of symplectomorphisms
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0010-2571&volume=79&issue=1&spage=58 http://www.math.technion.ac.il/~entov/My-Papers/index.html
arXiv:math.SG/0112012
Comm. Math. Helv. 79 (2004), N1, 58-104
Description: Results about commutator length of some groups arising in topology
Epstein, D.B.A.
Almost all subgroups of a Lie group are free
J. Algebra. 19(1971), 261-262
Availability: hardcopy
Erbas, C. and Sarkeshik, S. and Tanik, M.M.
Different Perspectives of the N-Queens Problem
DOI: 10.1145/131214.131227
Proceedings of the ACM 1992 Computer Science Conference, 1992
Availability: p99-erbas.pdf
Erdélyi, A.
Asymptotic Expansions
Dover, 1956; paperback, 108 pp.
Availability: hardcopy (book)
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Erdmann, Karin
On semisimple deformations of local semidihedral algebras
Arch. Math. 63 (1994), N6, 481-487
Description: Donald-Flanigan conjecture.
Availability: v52487x70438682r.pdf
Erdmann, Karen and Schaps, Malka
Deformation of tame blocks and related algebras
Israel Math. Con. Proc. 7 (1993), 23-
Description: Deformation of some group algebras (Domald-Flanigan conjecture).
Availability: hardcopy (book)
Erfanian, A.
A problem on growth sequences of groups
J. Austral. Math. Soc. Ser A 59 (1995), 283--286
A note on growth sequences of alternating groups
DOI: 10.1007/s00013-002-8244-y
Arch. Math. 78 (2002), N4, 257-262
Description: Growth sequence of a group G is a number of generators of G x ... x G (n times).
Ergun G.
Human sexual contact network as a bipartite graph
Physica A 308(2002), Nos. 1-4, 483-
Erickson, Theodore S.
The Lie structure in prime rings with involution
J. Alg. 21 (1972), 523-534
Availability: involution.pdf
Erickson, Theodore S. and Martindale, Wallace S. and Osborn, J. Marshall
Prime nonassociative algebras
Pacific J.M. 60(1975), 49-63
Availability: hardcopy
Erikesen, Eivind
An introduction to noncommutative deformations of modules
math.AG/0303166
Description: introduction to Laudal's theory
Eriksen, Eivind and Gustavsen, Trond S.
Computing connections on modules
math.AG/0602616
Abstract: We consider the notion of a connection on a module over a commutative ring, and deduce an obstruction calculus for determining if there exist such connections. The obstruction calculus is defined using Hochschild cohomology. However, in order to compute with Grobner bases, we need the non-trivial conversion to a description using free resolutions. We describe our implementation in Singular 3.0, available as the library conn.lib. Finally, we use the library to verify some known results and to obtain a new theorem for maximal Cohen-Macaulay (MCM) modules on isolated singularities. For a simple hypersurface singularity in dimension one and two, all MCM modules admit connections. Based on experiments, we conjecture that only the free MCM modules admit connections in dimension three.
Ermolaev, Yu. B.
Lie algebras of rank 1 with root system in the prime field
Izv. VUZ 120 (1972), N5, 38-50
Description: Extensions of sl(2) by V(p-2) + V(p-2) occur (later referred by Benkart & Osborn as "Ermolaev algebras").
Availability: hardcopy
Computation of a central element of the universal enveloping algbera of a Witt algebra
Izv. VUZ 19 (1975), N5, 20-
The minimal polynomial of the central element of the universal enveloping algebra of a Witt algebra
Izv. VUZ 20(1976), N10, 22-
Morozov's regularity theorem
Soviet Math. (Izv. VUZ) 35 (1991), N10, 5-10
Description: An interesting historical account of the Morozov's main work; a survey and references to subalgebras in semisimple classical Lie algebras.
Availability: hardcopy
Universalnoe kartanovskoe prodolzhenie
Izv. VUZ Mat. 1997, N11, 22-32
Proportionality of Lie words in classical Lie algebras
Izv. Vyssh. Uchebn. Zaved. Mat. 2002, no.9, 25--36
Russ. Math. (Izv. VUZ) 46 (2002), No. 9, 23-34
Zentralblatt: 1040.17003
Availability: 2002-proportionality.pdf
Integral bases of classical Lie algebras
Izv. Vyssh. Uchebn. Zaved. Mat. 2004, no.3, 16-25
Availability: 2004-integral.pdf
Ob odnoi realizacii kartanovskikh prodolzhenii
to appear
Ernst, T.
Les determinants generalises de Cauchy
Adv. Dyn. Syst. Appl. 1 (2006), no. 1, 59--77
Description: Related to Schur functor.
Availability: 1005.pdf
Ershov, Yu. L.
Profinite groups Profinite groups
DOI: 10.1007/BF01669608
Algebra and Logic 19 (1980), N5, 357-366
Description: Profinite groups of cohomological dimension 1.
Availability: 1980-profinite.pdf
Es Saadi, B. and Khakimdjanov, Yu. and Makhlouf, A.
Standard subalgebras of semisimple Lie algebras and computer-aided for enumeration
Ann. Math. Blaise Pascal 10 (2003), No.2, 315-326
MR 2031275
Zentralblatt: 1107.17005
Est, Willem Titus van
On Ado's theorem
Proc. Nederl. Akad. Wet. Ser. A 69 = Indag. Math. 28 (1966), 176-191
MR 34#1458
Zentralblatt: 0156.03901
Description: A new proof (p=0).
Availability: 201576.pdf (MR review)
Une démonstration de E. Cartan du troisième théorème de Lie
Actions hamiltoniennes de groupes. Troisième théorème de Lie, Sémin. Sud-Rhodan. Géom. VIII, Lyon/France 1986, Trav. Cours 27 (1988), 83-96
MR 951172
Zentralblatt: 0652.17002
Description: Inductive proof based on the fact that if a Lie algebra L has a central subalgebra C of dimension 1 such that L/C satisfies Lie's third theorem, then L satisfies Lie's third theorem, too. Relations with Ado's theorem.
Eswara Rao, S.
Iterated loop modules and a filtration for vertex representation of toroidal Lie algebras
Pacific J. Math. 171 (1995), N2, 511-528.
MR 1372242
Zentralblatt: 0867.17017
Partial classification of modules for Lie-algebra of diffeomorphisms of d-dimensional torus
arXiv:math.RT/0312024
Abstract: We consider the Lie-algebra of the group of diffeomorphisms of d-dimensional torus which is also known to be the algebra of derivations on a Laurent polynomial ring A in d commuting variables denoted by DerA. Larsson has constructed a large class of DerA modules based on gl_d modules which are also A modules. In this paper we prove that any irreducible (A, DerA) module with finite dimensional weight spaces has to come from Larsson's construction.
Irreducible representations of toroidal Lie algebras
DOI: 10.1016/j.jpaa.2005.01.011
J. Pure Appl. Algebra 202 (2005), N1-3, 102-117
arXiv:math/0212137
Eswara Rao, Senapati and Futorny, Vyacheslav
Irreducible modules for affine Lie superalgebras
math.RT/0311207
Eswara Rao, S. and Moody, R. V.
Vertex representations for n-toroidal Lie algebras and a generalization of the Virasoro algebra
Commun. Math. Phys. 159 (2004), 239-264
MR 1256988
Zentralblatt: 0808.17018
Etingof, Pavel
Quantum Knizhnik-Zamolodchikov equations and holomorphic vector bundles
Preprint
Availability: hardcopy
On integration in a space with complex dimension
Preprint, circa 1996
Availability: hardcopy
Exploring noncommutative algebras via deformation theory
arXiv:math.QA/0506144
Description: Lecture for general mathematical audience.
Etingof, P.I. and Frenkel, I.B.
Central extensions of current groups in two variables
DOI: 10.1007/BF02099419
Comm. Math. Phys. 3 (1994), 439-444
arXiv:hep-th/9303047
MR 1301619
Zentralblatt: 0822.22014
Description: Central extensions of some current algebras over Riemann surfaces (?)
Etingof, P.I. and Frenkel, I.B. and Kirillov, A.A. Jr.
Lectures on Representation Theory and Knizhnik-Zamolodchikov Equations
AMS, 1998
Description: Representations of classical simple, affine and quantum algebras.
Availability: Kolkhoz
Etingof, Pavel and Gan, Wee Liang and Ginzburg, Victor
Continuous Hecke algebras
Transformation Groups Issue: Volume 10, Numbers 3-4 Date: December 2005 Pages: 423 - 447
Availability: 767086052u3r215v.pdf
Etingof, Pavel and Grana, Matias
On rack cohomology
math.QA/0201290, 9pp.
Description: rack cohomology is some nicely defined cohomology of set with some bilinear operation; relations to Hopf algebras and quantization matters.
Etingof, Pavel and Kazhdan, David
Quantization of Lie bialgebras, I
DOI: 10.1007/BF01587938
Selecta Mathematica Volume 2, Number 1 / March, 1996 Pages 1-41
arXiv:q-alg/9506005
Quantization of Lie bialgebras, II
DOI: 10.1007/s000290050030
Selecta Mathematica Volume 4, Number 2 / August, 1998 Pages 213-231
arXiv:q-alg/9701038
Quantization of Lie bialgebras, III
arXiv:q-alg/9610030
Description: Quantization of bialgebras of g-valued functions on a punctures rational elliptic curve, where g is classical Lie algebra.
Quantization of Lie bialgebras, V
DOI: 10.1007/s000290050004
Selecta Math. 6 (200), N1, 105-130
arXiv:math.QA/9808121
Abstract: The goal of this paper is to define and study the notion of a quantum vertex operator algebra in the setting of the formal deformation theory and give interesting examples of such algebras. In particular, we construct a quantum vertex operator algebra from a rational, trigonometric, or elliptic R-matrix, which is a quantum deformation of the affine vertex operator algebra. The simplest vertex operator in this algebra is the quantum current of Reshetikhin and Semenov-Tian-Shansky.
Quantization of Lie bialgebras, VI. Quantization of generalized Kac-Moody algebras.
arXiv:math.QA/0004042
Etingof, Pavel and Kim, John and Ma, Xiaoguang
On universal Lie nilpotent associative algebras
arXiv:0805.1909
Euclid
The Thirteen Books of The Elements
URL: http://aleph0.clarku.edu/~djoyce/java/elements/toc.html http://techlibrary.ru/books.htm http://ivanik3.narod.ru/linksEvklidNachala.html http://www.math.ucsd.edu/~kgraehl/euclid/
Vol. 1-3, Dover, 1965
Availability: hardcopy (books); Kolkhoz
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Evans, Tyler J. and Fuchs, Dmitry
On the restricted Lie algebra structure for the Witt Lie algebra in finite characteristic
Funct. Anal. Appl. 36 (2002), N2, 140-144
arXiv:math.RT/0111271
Description: Technique is combinatorial and Young diagrams are involved.
A complex for the cohomology of restricted Lie algebras
Journal of Fixed Point Theory and Applications 3 (2008), no. 1, 159--179
Evans, G.C.
Functionals and Their Applications. Selected Topics Including Integral Equations
Dover, 1964; paperback, 147 pp.
Availability: hardcopy (book)
Evans, Tyler J.
Cohomology of Restricted Lie Algebras
Dissertation, 2001
arXiv:math.RT/0111090
Description: Including restricetd deformations of restricted Lie algebras (i.e. deforming also p-operations).
Availability: th.pdf
Everaert, Tomas and Gran, Marino
On low-dimensional homology in categories
Homology, Homotopy and Applications, Vol. 9 (2007), No. 1, pp.275-293
Abstract: The classical Stallings-Stammbach five-term exact sequence associated with a short exact sequence of groups is shown to exist in a general categorical context. This makes it possible to establish a new result relating low-dimensional homology and central series, which extends a well known result from the theory of groups.
Everaert, Tomas and Gran, Marino and Linden, Tim Van der
Higher Hopf formulae for homology via Galois Theory
DOI: 10.1016/j.aim.2007.11.001
Advances in Mathematics Volume 217, Issue 5, 20 March 2008, Pages 2231-2267
Abstract: We use Janelidze's Categorical Galois Theory to extend Brown and Ellis's higher Hopf formulae for homology of groups to arbitrary semi-abelian monadic categories.
Everaert, T. and Van der Linden, T.
Baer invariants in semi-abelian categories I: General theory
Theory Appl. Categories 12 (2004), No.1, 1-33
Abstract: Extending the work of Frohlich, Lue and Furtado-Coelho, we consider the theory of Baer invariants in the context of semi-abelian categories. Several exact sequences, relative to a subfunctor of the identity functor, are obtained. We consider a notion of commutator which, in the case of abelianization, corresponds to Smith's. The resulting notion of centrality fits into Janelidze and Kelly's theory of central extensions. Finally we propose a notion of nilpotency, relative to a Birkhoff subcategory of a semi-abelian category.
Baer invariants in semi-abelian categories II: Homology
Theory Appl. Categories 12 (2004), No.4, 195-224
Abstract: This article treats the problem of deriving the reflector of a semi-abelian category $\cal A$ onto a Birkhoff subcategory $\cal B$ of $\cal A$. Basing ourselves on Carrasco, Cegarra and Grandjean's homology theory for crossed modules, we establish a connection between our theory of Baer invariants with a generalization---to semi-abelian categories---of Barr and Beck's cotriple homology theory. This results in a semi-abelian version of Hopf's formula and the Stallings-Stammbach sequence from group homology.
Everett, C.J.
Iteration of the number theoretic function f(2n)=n, f(2n+1) = 3n+2
Adv. Math. 25(1977), 42-45
Description: Collatz conjecture
Availability: hardcopy
Ewell, John A.
On sums of triangular numbers and sums of squares
Amer. Math. Monthly 99(1992), No.8, 752-757
Availability: 4.pdf
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