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Gabber, Ofer and Kac, Victor G.
On defining relations of certain infinite-dimensional Lie algebras
BAMS 5 (1981), 185-189
Zentralblatt: 0474.17007
Description: Serre-type presentation of Kac-Moody. Reconciliation between Kac and Moody constructions. Exposition is in Kac's book.
Availability: S0273-0979-1981-14947-8.pdf
Gaiduk, T. N. and Sergeichuk, V. V. and Zharko, N. A.
Miniversal deformations of chains of linear mappings
Algebra and Discrete Mathematics, 2005, N1, 47-61
arXiv:0710.1278
Description: Develops Arnold's theme.
Gaines, Fergus J. and Laffey, Thomas J. and Shapiro, Helene M.
Pairs of matrices with quadratic minimal polynomials
DOI: 10.1016/0024-3795(83)80019-6
Linear Algebra and its Applications Volumes 52-53, July 1983, Pages 289-292
Abstract: Let A, B be n × n matrices over a field F, and suppose A, B have quadratic minimal polynomials. Then the algebra generated by A, B has dimension at most 2n-1 if n is odd and 2n if n is even. These bounds are exact.
Gainov, A.T.
Binary Lie algebras of characteristic two
Algebra and Logic 8 (1969), N5, 287-297
Algebra i Logika 8 (1969), N5, 505-522
Free commutative and free anticommutatibe products of algebras
Availability: hardcopy
The maximal spaces of skewsymmetric and symmetric matrices
Sib. Math. J. 32 (1991), 30-41
Galin, D.M.
On real matrices depending on parameters (in Russian)
UMN 27 (1972), N1, 241-242
Availability: GalinUMN71.pdf; hardcopy
Galitski, L.Yu. and Timashev, D.A.
On the classification of metabelian Lie algebras
J. Lie Theory 9 (1999), 125--156
Gallatin, G.M.
A useful formula for evaluating commutators
J. Math. Phys. 24(1983), 2564-
Description: Formulae expressing [A,f(B)] through commutators of A and B.
Availability: JMP02564.pdf
Gallier, Jean
Logarithms and Square Roots of Real Matrices
arXiv:0805.0245
Gambini, Alessandra
Algorithms for soluble subalgebras of finite dimensional lie algebras
DOI: 10.1016/0024-3795(88)90304-7
Linear Algebra and its Applications Volume 104 , June 1988, Pages 29-38
Gammella, Angela and Halbout, Gilles
A $G_\infty$-formality theorem in terms of graphs and associated Chevalley-Eilenberg-Harrison cohomology
Preprint IRMA 2003-015
Abstract: In 1997, M. Kontsevich proved the $L_\infty$ formality conjecture (which implies existence of star-products for any Poisson manifold) using graphs. A year later, D. Tamarkin gave another proof of a more general conjecture (for $G_\infty$ structures) using operads and cohomological methods. In this paper, we show how Tamarkin's construction can be done using graphs. For that, we introduce a generalization of Kontsevich graphs on which we define a ``Chevalley-Eilenberg-Harrison" complex. We show that this complex on graphs is trivial, which gives Tamarkin's formality theorem as a consequence, and from which one can find Kontsevich construction as a particular case.
Gan, Wee Liang
Koszual duality for dioperads
math.QA/0201074
Description: Dioperads for Lie bialgberas are the same as operads for Lie algebras.
Gantmacher, F.R.
Matrix Theory, 2 volumes
URL: http://www.krelib.com/matematika/452 http://www.vargin.mephi.ru/booksAlgebra.html http://techlibrary.ru/books.htm
AMS Chelsea Publ., 2000; hardcover, 374 + 276 pp.
Zentralblatt: 0927.15001|0927.15002
Availability: hardcopy (books)
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Gao, Shoulan and Jiang, Cuipo and Pei, Yufeng
The derivations, central extensions and automorphism group of the Lie algebra $W$
arXiv:0801.3911
Description: Semidrect product of Witt and its adjoint module.
Gao, Yun and Shang, Shikui
Universal coverings of Steinberg Lie algebras of small characteristic
DOI: 10.1016/j.jalgebra.2006.10.044
arXiv:math.QA/0512188
J. Algebra 311 (2007), N1, 216-230
Gao, Suo Gang and Zhang, Xin Lu
Ideals of some linear Lie superalgebras over commutative rings.
Acta Math. Sci. Ser. A Chin. Ed. 22 (2002), no. 4, 441--446
Gao, Jining
Chain extensions of D-algebras and their applications
math.QA/0311372
Abstract: In order to unify the methods which have been applied to various topics such as BRST theory of constraints, Poisson brackets of local functionals, and certain developments in deformation theory, we formulate a new concept which we call the {\it chain extension} of a $D$-algebra. We develop those aspects of this new idea which are central to applications to algebra and physics. Chain extensions may be regarded as generalizations of ordinary algebraic extensions of Lie algebras. Applications of our theory provide a new constructive approach to BRST theories which only contains three terms; in particular, this provides a new point of view concerning consistent deformations. Finally, we show how Lie algebra deformations are encoded into the structure maps of an sh-Lie algebra with three terms.
The Maurer-Cartan structure of BRST differential
math-ph/0410026
Abstract: ... for an important class of physical theories, we show that in fact the differential is a Chevalley-Eilenberg differential...
L_\infty algebra structures from Lie algebra deformations
DOI: 10.1016/j.jpaa.2006.03.016
math.QA/0410247
J. Pure Appl. Alg. 208 (2007), N3, 779-784
Abstract: ... how to kill the obstructions to Lie algebra deformations via a method which essentially embeds a Lie algebra into strong homotopy Lie algebra or L_\infty algebra...
Gao, Yun
On the Steinberg Lie algebras st_2(R)
Comm. Alg. 21 (1993), 3691-3706
MR 94m:17022
Description: R is not necessary associative; considerd conditions on R when sl_2(R) is a Lie algebra; H_2 and H_3 (sl_2(R), k) are studied (defining some generalization of HC_1(R))
Availability: hardcopy
Central extensions of nonsymmetrizable Kac-Moody algebras over commutative algebras.
Proc. Amer. Math. Soc. 121 (1994), no.1, 67-76
MR 94g:17046
Availability: gao.pdf
Steinberg unitary Lie algebras and skew-dihedral homology
DOI: 10.1006/jabr.1996.0013
J. Algebra 179 (1996), no.1, 261-304
MR 97b:17014
Leibniz homology of unitary Lie algebras
J. Pure Appl. Algebra 140 (1999), no.1, 33-56
MR 2000g:17002
Description: Second Leibniz cohomology, in lines with previous paper of Loday-Pirashvili.
Availability: hardcopy
The second Leibniz homology group for Kac-Moody Lie algebras
Bull. London Math. Soc. 32 (2000), 25-33
MR 2000i:17038
Description: Explicit calculation for all Kac-Moody algebras.
Availability: hardcopy
Representations of extended affine Lie algebras coordinatized by certain quantum tori.
Compositio Math. 123 (2000), no.1, 1-25
MR 2002c:17036
Garajeu, Daniela and Garajeu, Mihail
MATHEMATICA PACKAGES FOR COMPUTING PRINCIPAL DECOMPOSITIONS OF SIMPLE LIE ALGEBRAS AND APPLICATIONS IN EXTENDED CONFORMAL FIELD THEORIES
DOI: 10.1142/S012918310300419X
International Journal of Modern Physics C Year: 2003 Vol: 14 Issue: 1 (January 2003) Page: 1 - 27
Three-dimensional subalgebras of simple Lie algebras: a Mathematica package
DOI: 10.1088/0305-4470/37/3/011
J. Phys. A 37 (2004), no. 3, 677-691
Garcia, Esther
Combinatorics of the free Lie algebra and the symmetric group
Analysis, et cetera, Academic Press, 1990, 309-382
Zentralblatt: 0709.17003
Availability: CWI
Tits-Kantor-Koecher algebras of strongly prime Hermitian Jordan pairs
J. Algebra 277 (2004), no. 2, 559--571
Garcia, Esther and Gomez Lozano, Miguel
Jordan systems of Martindale-like quotients
J. Pure Appl. Algebra 194 (2004), N1-2, 127-145
Description: KKT construction: 3-graded algebras, derivations.
An elemental characterization of strong primeness in Lie algebras
DOI: 10.1016/j.jalgebra.2006.11.003
J. Algebra 312 (2007), N1, 132-141
Description: A Lie algebra L is prime and without absolute zero divisors iff [a,[b,L]] = 0 implies a=0 or b=0.
Garcia, Esther and Neher, Erhard
Tits-Kantor-Koecher Superalgebras of Jordan Superpairs Covered by Grids
Comm. Algebra 31, N7, 3335-3375
Abstract: In this paper we describe the Tits-Kantor-Koecher superalgebras associated to Jordan superpairs covered by grids, extending results from Neher (Neher, E. (1996). Lie algebras graded by 3-graded root systems and Jordan pairs covered by a grid. Amer. J. Math. 118; 439-491) to the supercase. These Lie superalgebras together with their central coverings are precisely the Lie superalgebras graded by a 3-graded root system.
GARC´IA-PLANAS, M. I. and MAILYBAEV, A. A.
REDUCTION TO VERSAL DEFORMATIONS OF MATRIX PENCILS AND MATRIX PAIRS WITH APPLICATION TO CONTROL THEORY
SIAM J. MATRIX ANAL. APPL. 2003 Vol. 24, No. 4, pp. 943-962
Availability: GarciaMailybaev2003.pdf
Garcia-Planas, M. Isabel and Sergeichuk, Vladimir V.
Simplest miniversal deformations of matrices, matrix pencils, and contragredient matrix pencils
Lin. Alg. Appl. 302-303 (1999), 45-61
arXiv:0710.0946
Description: Another development of Arnold's theme of versal deformations.
Garcia-Rio, E. and Haji-Badali, A. and Vazquez-Abal, M.E. and Vazquez-Lorenzo, R.
Lorentzian 3-manifolds with commuting curvature operators
DOI: 10.1142/S0219887808002941
Int. J. Geom. Meth. Modern Phys. 5 (2008), N4, 557-572
Availability: 021105353987.pdf
Garcia Roman, Socorro and Garcia Roman, Manuel
Effective computation of Tor_k(M, N)
Comm. Algebra 33(2005), N12, 4587-4594
Description: Over associative algebras.
Garcia-Vergnolle, Lucia and Remm, Elisabeth
Complex structures on quasi-filiform nilpotent Lie algebras
arXiv:0805.1833
Gardner, Martin
Snarks, Boojums and other conjectures related to the four-color-map theorem
Scientific American, April 1976 (?)
Availability: snarks.djvu [without last pages]
Gardner, B.J. and Osborn, J.M. and Shestakov, I.P.
Varieties and tensor products
Nova J. Algebra Geom. 1 (1992), N4, 347-357
MR 94c:17001
Description: When a tensor product of two algebras from some varieties, lies again in one of these varieties?
Availability: hardcopy
Gardner, B.J. and Wiegandt, R.
Radical theory of rings
M. Dekker, 2003, 408 pp.
Availability: 2003-radical.pdf
Garey, M.R. and Johnson, D.S.
Computers and Intractability. A Guide to the Theory of NP-Completness
Bell Telephone Laboratories, 1979
Availability: np.djvu
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Gargoubi, H. and Mathonet, P. and Ovsienko, V.
Symmetries of modules of differential operators
DOI: 10.2991/jnmp.2005.12.3.4
J. Nonlin. Math. Phys. 12 (2005), N3, 348-380
Zentralblatt: (me)
Availability: hardcopy
Gargoubi, H. and Ovsienko, V.
Space of linear differential operators on the real line as a module over the Lie algebra of vector fields
arXiv:dg-ga/9602004
Modules of differential operators on the real line
Funct. Anal. Appl. 35 (2001), no.1, 13-18
Zentralblatt: (me)
Description: "Tensor densities" are involved.
Availability: hardcopy
Garibaldi, Skip R.
Structurable algebras and groups of types E6 and E7
arXiv:math.RA/9811035
Description: KKT construction (among all)
Groups of type E7 over arbitrary fields
DOI: 10.1081/AGB-100002415
arXiv:math.AG/9811056
Comm. Alg. 29 (2001), N6, 2689-2710
Description: KKT construction (among all)
Availability: 100002415.pdf (paper)
An invariant of simple algebraic groups
arXiv:math.GR/0204159
Description: Forms of algebraic groups of type D_4 and E_6.
The characteristic polynomial and determinant are not ad hoc constructions
arXiv:math.LA/0203276
Amer. Math. Monthly 111 (2004), no. 9, 761--778
Abstract: This note gives a canonical construction of the characteristic polynomial as the minimal polynomial of a "generic" matrix. This approach works not just for matrices but also for a very broad class of algebras including the quaternions, all central simple algebras, and Jordan algebras.
Availability: hardcopy (journal)
Vanishing of trace forms in low characteristics
arXiv:0712.3764
Description: Lie algebra of type E8 over a field of characteristic 5 does not have a quotient trace form.
Orthogonal involution on algebras of degree 16 and the Killing form of E8
arXiv:0712.4133
Description: All E_8's over number fields.
Garibaldi, Skip and Gille, Philippe
Algebraic groups with few subgroups
Linear Algebraic Groups and Related Structures Preprint, 2008
Description: "Almost abelian" (i.e. having no closed connected subgroups other then maximal tori) simple algebraic groups (e.g., there are such groups of type E_6-E_8, bit not of types G_2 and F_4). This seems to outperform any Lie-algebraic investigations on minimal nonabelian algebras.
Availability: hardcopy
Garibaldi, Skip and Merkurjev, Alexander and Serre, Jean-Pierre
Cohomological Invariants in Galois Cohomology
AMS, 2003, 168 pp.
Garibaldi, Skip and Petersson, Holger P.
Groups of outer type E6 with trivial Tits algebras
URL: http://www.mathcs.emory.edu/~skip/preprints.html http://www.mathematik.uni-bielefeld.de/LAG/man/209.html http://www.uibk.ac.at/mathematik/loos/jordan/archive/GPe/index.html
DOI: 10.1007/s00031-006-0051-2
arXiv:math.GR/0511229
Transform. Groups 12 (2007), no. 3, 443--474
Description: Tits construction. Albert algebras. When a group is isotropic?
Garkusha, Grigory
Homotopy theory of associative rings
DOI: 10.1016/j.aim.2006.12.013
math.KT/0608482
Advances in Mathematics Volume 213, Issue 2, 20 August 2007, Pages 553-599
Garland, Howard
Dedekind's \eta-function and the cohomology of infinite dimensional Lie algebras
PNAS 72 (1975), no.7, 2493-2495
Description: Cohomology of g\otimes t^{-1}C[t]. Later generalized by Garland and Lepowsky to more general Kac-Moody setting.
Availability: hardcopy
The arithmetic theory of loop groups
Publ. IHES 52 (1980), 5-136
Availability: hardcopy
Garland, Howard and Lepowsky, James
Lie algebra homology and the Macdonald-Kac formulas
Inv. Math. 34 (1976), 37-76
Zentralblatt: 0358.17015
Description: Related to current algebras. Homology of minus-part of Kac-Moody algebra (generalizing the Kostant's result about homology of nilradical of Borel subalgebra).
Availability: hardcopy
Garner, Lynn E.
On the Collatz 3n + 1 algorithm
Proc. AMS 82 (1981), No.1, 19-22
Availability: 0-150.pdf
Gartside, P. M. and Knight, R. W.
Ubiquity of free subgroups
DOI: 10.1112/S0024609303002194
Bull. LMS 35 (2003), 624-634
Abstract: Necessary and sufficient conditions are given for a Polish topological group to be `almost free'. It is deduced that the existence of one free subgroup of a Polish group can lead to the existence of many free subgroups of maximal rank. Applications are given to permutation groups, profinite groups, Lie groups and unitary groups.
Availability: S0024609303002194a.pdf
Garvín, Antonio and Lechuga, Luis
The computation of the Betti numbers of an elliptic space is a NP-hard problem
Topology and its Applications Volume 131, Issue 3 , 1 July 2003, Pages 235-238
Abstract: Let S a 1-connected space such that and are both finite-dimensional. Then, using the Sullivan model as a codification for S, we prove that the computation of the Betti numbers of S is a NP-hard problem.
Gasper, G. and Rahman, M.
Basic Hypergeometric Series
Mir, 1993 (Russian translation from Cambridge Univ. Press, 1990); hardcover, 349 pp.
Availability: hardcopy (book); absent on ozon
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Gastaminza, S. and Pena, J.A. de la and Platzeck, M.l. and Redondo, M.J. and Trepode, S.
Finite dimensional algebras with vanishing Hochschild cohomology
DOI: 10.1006/jabr.1998.7614
J. Alg. 212 (1999), N1, 1-16
Description: In terms of quivers.
Gateva, T.V.
On the complexity of the variety generated by the tensor product of algebras
Vestn. MGU Mat. Mekh 1980, N2, 47-50
Description: Complexity of a variety is a number n such that identities in that variety a n-powers of identities of a matrix algebra.
Estimate of the complexity of the variety generated by the tensor product of algebras
Dokl. Bulg. Akad. Nauk 35 (1982), N12, 1623-1626
Availability: Central Icelandic library.
Gateva-Ivanova, Tatiana and Latyshev, Victor
On recognisable properties of associative algebras
Computational Aspects of Commutative Algebra (from a special issue of the Journal
of Symbolic Computation) (ed. L. Robbiano), Academic Press, 1989, 237-254
Description: Recognizable = could be established algorithmically.
Availability: Kolkhoz
Gatheral, James and Epelbaum, Yonathan and Han, Jining and Laud, Kishor and Lubovitsky, Olga and Kant, Elaine and Randall, Curt
Implementing option-pricing modles using software synthesis
IEEE Computing Sci. Eng. 1(1999), N6, 54-64
Availability: hardcopy
Gatica, Maria Andrea and Rey, Andrea Alejandra
Computing the Hochschild cohomology groups of some families of incidence algebras
DOI: 10.1080/00927870600549543
Comm. Algebra 34 (2006), no. 6, 2039--2056
Gaucher, Philippe
Lambda-opérations sur l'homologie d'une algèbre de Lie de matrices.
URL: http://www-irma.u-strasbg.fr/irma/publications/1994/94011.shtml http://www.springerlink.com/openurl.asp?genre=article&issn=0920-3036&volume=13&issue=2&spage=151
Prebubl. IRMA, 1994, 011
K-Theory 13 (1998), N2, 151-167
Abstract: One extends Loday-Procesi lambda-operations from the cyclic homology of A to the homology of the Lie algebra gl_\infty(A) using exterior powers of matrices. In this way, we obtain an interpretation of this lambda-operations, originally defined in combinatorial terms, in terms of matrix operations. One shows a formula giving their behavior with respect to the direct sum of matrices. It uses the coproduct and the structure of ring objet induced by the tensor product of matrices.
Gaudier, Henri and Massy, Richard
Effective computation of the 2-cocycles for a split policyclic group
Preprint
Description: Examples of concrete computations of cocycles from resolutions from group presentations.
Availability: amshgrm.ps
Gauger, Michael A.
On the classification of metabelian Lie algebras
DOI: 10.2307/1996506
Trans. Amer. Math. Soc. 179 (1973), 293-329
MR 48#4066
A characterization of the Borel subalgebras of semi-simple Lie algebras among all solvable Lie algebras
DOI: 10.1215/S0012-7094-76-04302-7
Duke Math. J. 43 (1976), N1, 11-17
MR 0393150
Zentralblatt: 0375.17004
Duality theories for metabelian Lie algebras. I, II
DOI: 10.2307/1997044
TAMS 187 (1984), N1, 89-102; 1975
Gavioli, Norberto and Monti, Valerio and Young, David S.
Metabelian Thin Lie Algebras
DOI: 10.1006/jabr.2001.8752
Journal of Algebra Volume 241, Issue 1 , 1 July 2001, Pages 102-117
Gavish, Matan and Peled, Amnon and Chor, Benny
Genetic code symmetry and efficient design of GC-constrained coding sequences
DOI: 10.1093/bioinformatics/btl317
Bioinformatics 2007 23(2):e57-e63
Availability: decode
Gawedzki, Krzysztof
Lecture 1. Simple functional integrals. Lecture 2. Axiomaic approaches to quantum field theory
Lecture notes, circa 1996.
Availability: hardcopy
Geer, Nathan
Etingof-Kazhdan quantization of Lie superbialgebras
math.QA/0409563
Gein, Alexander G.
Lie algebras that can be covered by ideals and abelian subalgebras
Mat. Zapiski Ural. Gos. Univ. 9 (1974), no.1, 11-14 (in Russian)
MR 52#10820
Zentralblatt: 0322.17005
Description: Finite-dimensional Lie algebras in which each maximal subalgebra is either ideal or abelian.
Availability: hardcopy
Semimodular Lie algebras
DOI: 10.1007/BF00967564
Siber. Math. J. 17 (1976), N2, 189-193
Zentralblatt: 0342.17010
Availability: J8382N8745107411.pdf
Proektirovaniya algebr Lie characteristiki 0
Izv. Vuz. 1978, N4, 26-31
On degress of solvability of lattice-isomorphic Lie algebras
Algebraicheskie Sistemy i ikh Mnogoobraziya, Mat. Zapiski 13 (1982), N1, 7-15
Zentralblatt: 0507.17005
Description: If solvable Lie algebras are lattice-isomorphic, then their degress of solvability differ by at most one.
Modular subalgebras and projection of locally finite-dimensional Lie algebras of characteristic 0
Mat. Zapiski Ural. Gos. Univ. 13 (1983), no.3, Algebraich. Sistemy. Mnogoobraziya. Reshetki Podsistem, 39-51 (in Russian)
MR 86c:17007
Minimal nonabelian Lie algebras of prime characteristic
C. R. Acad. Bulgare Sci. 37 (1984), no.10, 1291-1293
MR 88b:17017
Availability: hardcopy
Minimal nonabelian Lie algebras of prime characteristic
Mat. Zapiski Ural. Gos. Univ. 13 (1984), no.4, 42-47
MR 87c:17010
Minimal noncommutative and minimal nonabelian algebras
Comm. Algebra 13 (1985), N2, 305-328
MR 86d:17007
Availability: hardcopy
Modular rule and relative complements in the lattice of subalgebras of a Lie algebra
Soviet Math. (Izv. VUZ) 31 (1987), no.3, 22-32
Availability: hardcopy
Lie algebras with constraints on subalgebras
Sverdlovsk, 1989 (in Russian)
Zentralblatt: 1098.17500
Availability: hardcopy
Gein, A.G. and Kuznetsov, S.V. and Mukhin, Yu.N.
On minimal nonilpotent Lie algebras
Matematicheskie Zapiski (Sverdlovsk) 8 (1972), Tetrad' 3, 18-27 (in Russian)
Availability: hardcopy
Gein, Alexander G. and Mukhin, Yu.N.
Poluabelevy algebry Lie
Mat. Issled. (Kishinev) 10 (1975), N1, 78-93
Description: Lie algebras all whose subalgebras are either ideal or abelian or nilpotent.
Availability: hardcopy
Gein, A.G. and Tolstov, F.L.
Solvability of Lie algebras that are decomposable into a sum of two nilpotent subalgebras (in Russian)
Izv. VUZ 1989, N9, 18-22
Gelander, T.
Notes on uniform exponential growth and Tits alternative
arXiv:0803.3383
Gelbart, Stephen
Automorphic forms on the metaplectic group
Preprint, Cornell Univ., 1974
Availability: automorphic-1974.djvu
Gelfand, I.M. and Dorfman, I.Ya.
The Schouten bracket and Hamiltonian operators
Funk. Anal. Prilozh. 14 (1980), N3, 71-74
Availability: hardcopy
Hamiltonian operators and the classical Yang-Baxter equation
Funk. Anal. Prilozh. 16 (1982), N4, 1-9
Availability: hardcopy
Gelfand, I.M. and Gelfand, S. and Retakh, V. and Wilson, R.
Quasideterminants
DOI: 10.1016/j.aim.2004.03.018
arXiv:math.QA/0208146
Adv. Math. 193(2005), N1, 56-141
Zentralblatt: 1079.15007
Description: (Quasi)determinant over noncommutative rings.
Availability: hardcopy
Factorizations of polynomials over noncommutative algebras and sufficient sets of edges in directed graphs
Lett. Math. Phys. 74 (2005), N2, 153 - 167
Abstract: To directed graphs with unique sink and source we associate a noncommutative associative algebra...
Gelfand, I.M. and Kalinin, D.I. and Fuchs, D.B.
Cohomology of the Lie algebra of Hamiltonian formal vector fields
Funct. Anal. Appl. 6 (1972), 193-196
MR 47#1088
Zentralblatt: 0259.57023
Availability: hardcopy
Gelfand, I.M. and Kazhdan, D.A.
Some problems of differential geometry and the calculation of cohomology of Lie algebras of vector fields
Sov. Math. Dokl. 12(1971), 1367-1370
Dokl. Akad. Nauk SSSR 200(1971), 269-272
(absent)
Zentralblatt: 0238.58001
Gelfand, S.I. and Manin, Yu.I.
Homological Algebra
Springer, 1999 (reprint of Algebra V, Encyclopaedia of Mathematical Sciences, Vol. 38, 1994; translation from Russian, VINITI, 1989); paperback, 222 pp.
Availability: hardcopy (book); Kolkhoz
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Methods of Homological Algebra
URL: http://www.justpasha.f2s.com/books/metody-1.djvu http://techlibrary.ru/books.htm http://ef12517-2.tu-sofia.bg/Desislav Todorov/Frames/Books/Mathematics/Algebra/
Springer
Availability: Kolkhoz (in Russian)
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Gelfand, I.M. and Mathieu, O.
On the cohomology of the Lie algebra of Hamiltonian vector fields
J. Funct. Anal. 108 (1992), No.2, 347-360
MR 93g:17039
Zentralblatt: 0783.17009
Abstract: The work of Gelfand and Fuchs [Funkt. Anal. Appl. 4, 110-116 (1970); Zbl 0208.514)] concerning the cohomology of the Lie algebra of all vector fields on a manifold is extended to the cohomology of the Lie algebra of all Hamiltonian vector fields on a symplectic manifold. The case of an even-dimensional algebraic torus is treated in detail.
Availability: hardcopy
Gelfand, I.M. and Ponomarev, V.A.
Indecomposable representations of the Lorentz group
Rus. M. Surv. 23(1968), N2, 1-59
Description: Some representation theory problems reduced to linear algebra problems.
Gelfand, Israel and Retakh, Vladimir and Serconek, Shirlei and Wilson, Robert Lee
On a class of algebras associated to directed graphs
arXiv:math.QA/0506507
Selecta Math. 11 (2005), N2, 281-295
Abstract: To any directed graph we associate an algebra with edges of the graph as generators and with relations defined by all pairs of directed paths with the same origin and terminus.
Gelfand, Israel and Retakh, Vladimir and Wilson, Robert Lee
Quaternionic quasideterminants and determinants
Lie Groups and Symmetric Spaces. In Memory of F.I. Karpelevich (ed. S.G. Gindikin), AMS Transl. 210 (2003), 111-
Availability: Kolkhoz (whole book)
Gelfand, I.M. and Tsygan, B.L.
On the localization of topological invariants
Preprint
Availability: hardcopy
Gelfand, I.M.
Lectures on Linear Algebra
URL: http://www.mccme.ru/free-books/linalg/gelfand.html http://techlibrary.ru/books.htm http://www.newlibrary.ru/book/gelfand_i_m_/lekcii_po_lineinoi_algebre.html http://da8.boom.ru/ct/algebra.htm http://lib.prometey.org/?id=14847&page=2
5th ed., Dobrosvet, Moscow, 1998 (in Russian)
Availability: Kolklhoz
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Gelfand, S.I.
Weil's representation of the Lie algebra of type G_2, and representations of SL_3 connected with it
Funct. Anal. Appl. 14 (1980), N1, 40-41
Description: Representation of G_2 by differential operators in the space of functions in 3 variables.
Geller, S. and Maloo, Alok Kumar and Patil, D. P. and Roberts, L. G.
Kähler Differentials of Affine Monomial Curves
Beiträge zur Algebra und Geometrie Vol. 41, No. 1, pp. 67-84 (2000)
Description: Kahler diffs of groups algebras of some monoids
Gelman, B. D.
A generalized implicit function theorem
URL: http://www.ingenta.com/isis/searching/ExpandTOC/ingenta;jsessionid=?issue=infobike://klu/faia/2001/00000035/00000003&index=3 http://dx.doi.org/10.1023/A:1012322727547
Funct. Anal. Appl. 35(2001), N3, 183-188
Description: Generalization of the implicit function theorem, requiring only surjectivity of derivative (and not invertibility).
Availability: fulltext.pdf
Generalov, A.I.
Hochschild cohomology of dihedral-type algebras. I. The D(3K) series in characteristic 2
Algebra i Analiz 16 (2004), no. 6, 53--122
MR 2117449 (me)
Availability: hardcopy
Hochschild cohomology of the integral group ring of the dihedral group. I: Even case
DOI: 10.1090/S1061-0022-08-01018-2
Algebra i Analiz, tom 19 (2007), nomer 5
St. Petersburg Math. J. 19 (2008), 723-763
MR 2381942
Generalov, Alexander and Kosmatov, Nikolai
Projective resolutions and Yoneda algebras for algebras of dihedral type
Algebr. Represent. Theory 10 (2007), no. 3, 241--256
MR 2008h:16009
Description: Using computer algebra.
Genov, Georgi K.
Polynomial identities in a tensor product of Lie algebras (in Russian)
Bulgar. Akad. Nauk. Izv. Mat. Inst. 15 (1974), 291-300
MR 51#10394
Zentralblatt: 0338.17003
Description: The tensor product of two Lie algebras always posseses an identity in the class of nonassociative algebras.
Gentili, Graziano and Struppa, Daniele C. and Vlacci, Fabio
The fundamental theorem of algebra for Hamilton and Cayley numbers
DOI: 10.1007/s00209-007-0254-9
Mathematische Zeitschrift Volume 259, Number 4 / August, 2008 Pages 895-902
Gentle, James
Matrix Algebra. Theory, Computations, and Applications in Statistics
DOI: 10.1007/978-0-387-70873-7
Springer, 2007
Gerdt, Vladimir P. and Kornyak, Vladimir V.
Lie algebras and superalgebras defined by a finite number of relations: computer analysis
J. Nonlinear Math. Phys. 2 (1995), no. 3-4, 367-373
MR 96i:17001
An implementation in C of an algorithm for construction of finitely presented Lie superalgebras.
Comput. Sci. J. Moldova 4 (1996), no. 3, 399-427
MR 99m:17001
Construction of finitely presented Lie algebras and superalgebras
DOI: 10.1006/jsco.1996.0016
J. Symbolic Comput. 21 (1996), no. 3, 337-349
Preprint JINR 95-353
MR 97f:17003
An algorithm for analysis of the structure of finitely presented Lie algebras
Discrete Mathematics and Theoretical Computer Science 1 (1997), 217-228
Abstract: Algorithm for construction of basis of a Lie algebra according to its presentation.
Programma dlya postroeniya polnoi sistemy sootnoshenii, bazisnykh elementov i tablicy kommutatorov konechno predstavlennykh algebr Lie i superalgebr Lie
Programmirovanie 1997, N3, 58-71
Gerdt, V. P. and Robuk, V. N. and Severyanov, V. M.
Construction of finitely presented Lie algebras
Zh. Vychisl. Mat. i Mat. Fiz. 36 (1996), no. 11, 20--34
translation in Comput. Math. Math. Phys. 36 (1996), no. 11, 1493--1505 (1997)
MR 98b:17005
MR Review: The authors describe an algorithm for computing a basis of a Lie algebra defined by a finite system of generators and relations. Example computations took much more machine time compared with a different algorithm developed by G. H. M. Roelofs ["The LIESUPER package for REDUCE", Mem. 943, Univ. Twente, Enschede, 1991; per bibl.].
Gerdt, V. P. and Zinin, M. V.
Involutive method for computing Gröbner bases over \mathbbF2 F2
DOI: 10.1134/S0361768808040026
Programming and Computer Software Volume 34, Number 4 / July, 2008 Pages 191-203
Germoni, Jerome
Indecomposable representations of osp(3,2), D(2,1,\alpha) and G(3)
Manuscript, September 1999
Availability: G(3)(Germoni).ps
On the classification of admissible representations of the Virasoro algebra
Lett. Math. Phys. 55 (2001), no. 2, 169--177; erratum: 59 (2002), no. 3, 277
MR 2002i:17033
Geronimus, A. Yu.
Cohomologies of groups in categories
DOI: 10.1007/BF01076129
Funct. Anal. Appl. 2 (1968), N3, 259-260
Gerritzen, L. and Holtkamp, R.
Co-Addition for free Non-Associative Algebras and the Hausdorff Series
math.RA/0207083
Description: Generalizations of the series exp and log to noncommutative non-associative and other types of algebras were regarded by M.Lazard, and recently by V.Drensky and L.Gerritzen. There is a unique power series exp(x) in one non-associative variable x such that exp(x)exp(x)=exp(2x), exp'(0)=1. We call the unique series H=H(x,y) in two non-associative variables satisfying exp(H)=exp(x)exp(y) the non-associative Hausdorff series, and we show that the homogeneous components of H are primitive elements with respect to the co-addition for non-associative variables. We describe the space of primitive elements for the co-addition in non-associative variables using Taylor expansion and a projector onto the algebra A_0 of constants w.r.t. the partial derivations, which contains all non-linear primitive elements. By a theorem of Kurosh, A_0 is a free algebra. We describe a procedure to construct a free algebra basis which consists of primitive elements.
Gerstenhaber, Murray
On the construction of division rings by the deformation of rings
Proc. Nat. Acad. Sci. USA 55 (1966), N4, 690-692
On nilalgebras and linear varieties of nilpotent matrices. I
DOI: 10.2307/2372773
Amer. J. Math. 80 (1958), 614-622
Availability: 2.pdf
On nilalgebras and linear varieties of nilpotent matrices. II
Duke Math. J. 27 (1960), no.1, 21-31
Availability: 1077468913.pdf
On nilalgebras and linear varieties of nilpotent matrices. III
Ann. Math. 70 (1959), 167-205
Availability: 3.pdf
On nilalgebras and linear varieties of nilpotent matrices, IV
The Annals of Mathematics, Second Series, Vol. 75, No. 2 (Mar., 1962), pp. 382-418
The cohomology structure of an associative ring
Ann. Math. 78 (1963), 267-288
Description: That is where the graded Lie superalgebra structure on H^*(A,A) for associative A was introduced.
Availability: gerst-coho.pdf; hardcopy
A uniform cohomology theory for algebras
Proc. Natl. Acad. Sci. USA 51 (1964), 626-629
Zentralblatt: 0166.04205
Description: A universal cohomology theory for algebras in any variety as classes of n-fold singular extensions. This coincides with classical cohomology in Lie and associative cases. Comparison with other known theories.
Availability: 0-150.pdf
On the deformation of rings and algebras
DOI: 10.2307/1970484
Ann. Math. 79 (1964), N1, 59-103
Zentralblatt: 0123.03101
Description: Classics.
Availability: hardcopy
On the deformation of rings and algebras. II
DOI: 10.2307/1970528
Ann. Math. 84 (1966), No.1, 1-19
Availability: hardcopy
The third cohomology group of a ring and the commutative cohomology theory
BAMS (?) circa 1967
Description: Related to Harrison cohomology.
Availability: hardcopy
The obstruction to an automorphism of a filtered ring
BAMS 74 (1968), 695-697
Description: Deformation theory.
On the deformation of rings and algebras. III
DOI: 10.2307/1970553
Ann. Math. 88 (1968), 1-34
Availability: hardcopy; 0.pdf
On modular field extensions
J. Alg. 10 (1968), 478-484
Availability: science-2.pdf
On the deformation of rings and algebras. IV
Ann. Math. pp.257-276
Description: Jump deformations (filtered deformations are jump deformations). In p=0, the cohomology of nontrivially jump deformed algebra necessary strictly decreases.
Availability: hardcopy
Deformation of towers of algebras and quantized intersection cardinality functions
Lett. Math. Phys. 43 (1998), N2, 87-103
Developments from Barr's thesis
J. Pure Appl. Alg. 143 (1999), 205-220
Zentralblatt: 0997.16003
Description: "... today we can define cohomology groups for practically anything by means of operads, cf. Gunzburg-Kapranov". A survey on the theme of Barr's decomposition of Hochschild cohomology of commutative rigs into summands one of which is Harrison cohomology and other (recent) Gerstenhaber's works.
Availability: Barrfest.ps; hardcopy
The principal element of a Frobenius Lie algebra
arXiv:0801.4808
Gerstenhaber, M. and Giaquinto, A.
Boundary solutions of the classical Yang-Baxter equation
DOI: 10.1023/A:1007363911649
Lett. Math. Phys. 40 (1997), N4, 337-353
arXiv:q-alg/9609014
Description: Related to Lie algebras having a nondegenerate 2-cocycle.
Compatible deformations
Trends in the Representation Theory of Finite Dimensional Algebras (ed. E.L.Green and B.Huisgen-Zimmerman), Contemp. Math. 229 (1998), 159-168
Zentralblatt: 0933.16025
Description: Donald-Flanigan conjecture fails for 8-element quaternion group (but this is apparently wrong).
Availability: varalg.pdf; hardcopy (both the separate paper and book)
Graphs, Frobenius functionals, and the classical Yang-Baxter equation
arXiv:0808.2423
Description: Frobenius Lie algebras.
Gerstenhaber, Murray and Giaquinto, Anthony and Schack, S.D.
Diagrams of Lie algebras
DOI: 10.1016/j.jpaa.2004.08.022
J. Pure Appl. Algebra 196 (2005), N2-3, 169-184
Zentralblatt: pre02153391
Description: Deformations and cohomology. Abstract nonsense. Results of Fregier claimed to be a particular case.
Availability: sdarticle.pdf
Gerstenhaber, Murray and Giaquinto, Anthony and Schaps, Mary E.
The Donald-Flanigan problem for finite reflection groups
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0377-9017&volume=56&issue=1&spage=41 http://www.cs.biu.ac.il/~mschaps/math.html
Lett. Math. Phys. 56 (2001), N1, 41-72
arXiv:math/0008058
Zentralblatt: 1003.16025
Availability: l5w088713173mq24.pdf
Gerstenhaber, Murray and Green, David J.
A group-theoretic consequence of the Donald-Flanigan conjecture
DOI: 10.1006/jabr.1994.1156
J. Alg. 166 (1994), 356-363
MR 95f:20015
Gerstenhaber, M. and Rothaus, O.S.
The solution of sets of equations in groups
Proc. Natl. Acad. Sci. USA 48, 1531-1533 (1962)
Zentralblatt: 0112.02504
Description: Criterion for solution of system of equations in a subgroup of a compact connected Lie groups, generalizing the linear-algebraic criterion.
Gerstenhaber, Murray and Schack, Samuel D.
On the deformation of diagrams of algebras
Contemp. Math. 13 (1982), 193-197
Zentralblatt: 0507.18005
Simplicial cohomology is Hochschild cohomology
JPAA 30 (1983), 143-156
Zentralblatt: 0527.16018
Availability: There is a functor from locally finite simplicial complexes to associative unital; algebras preserving (respective) cohomology.
On the deformation of algebra morphisms and diagrams
DOI: 10.2307/1999369
TAMS 279 (1983), 1-50
On the cohomology of an algebra morphism
J. Algebra 95 (1985), 245-262
Zentralblatt: 0595.16021
Description: Probably generalized later for the setting of "presheaves of algebras".
Relative Hochschild cohomology, rigid algebras, and the Bockstein
DOI: 10.1016/0022-4049(86)90004-6
JPAA 43 (1986), 53-74
Zentralblatt: 0603.16021
Description: Associative rigid algebras in positive charactresitic with H^2 not 0. For p=0, geometric rigidity is equivalent to formal rigidity.
Availability: 1986-relative.pdf
A Hodge-type decomposition for commutative algebra cohomology
JPAA 48 (1987), 229-247
Availability: hodge.djvu
Sometimes H^1 is H^2 and discrete groups deforms
Contemp. Math. 74 (1988), 149-169 (ed. W.M.Goldman and A.H.Magid)
Algebraic cohomology and deformation theory
Deformation theory of algebras and structures and applications, Kluwer, 1988, 11-264
Zentralblatt: 0676.16022
Description: This is "The" deformation theory survey (actually a book).
Availability: hardcopy
Bialgebra cohomology, deformations, and quantum groups
Proc. Natl. Acad. Sci. USA 87 (1990), No.1, 478-481
Zentralblatt: 0695.16005
Description: Introduction of cohomology and deformation theory of bialgebras (double complex).
The shuffle bialgebra and the cohomology of commutative algebras
J. Pure Appl. Algebra 70 (1991), No.3, 263-272
Zentralblatt: 0728.13003
Availability: gs.pdf
Algebras, bialgebras, quantum groups, and algebraic deformations
Deformation theory and quantum groups with applications to mathematical physics, Contemp. Math. 134 (1992), 51-92
Zentralblatt: 0788.17009
Availability: hardcopy (book); Kolkhoz
Gerstenhaber, N. and Schaps, M.E.
The modular version of Maschke's theorem for normal abelian p-Sylows
JPAA 108 (1996), 257-264
Hecke algebras, U_q(sl_n), and the Donald-Flanigan conjecture for S_n
URL: http://www.ams.org/tran/1997-349-08/S0002-9947-97-01761-3/home.html http://links.jstor.org/sici?sici=0002-9947(199708)349%3A8%3C3353%3AHAATDC%3E2.0.CO%3B2-2
TAMS 349 (1997), 3353-3371
arXiv:q-alg/9502016
Description: Braid-group-like presentation of S_n is employed!
Availability: hardcopy
Getzler, Ezra
Cyclic homology and the Beilinson-Manin-Schechtman central extension
Proc. Amer. Math. Soc. 104 (1989), 729-734
Description: Cenral extensions of Lie algebra of differential operators, after some Loday-Quillen considerations.
Availability: centre.pdf
Cartan homotopy formulas and the Gauss-Manin connection in cyclic homology
Israel Math. Conf. Proc. 7 (1993), 65-
Availability: hardcopy (both preprint & book)
The homology groups of some two-step nilpotent Lie algebras associated to symplectic vector spaces
arXiv:math.KT/9903147
A Darboux theorem for Hamiltonian operators in the formal calculus of variations
Duke Math. J. 111 (2002), no. 3, 535-560
arXiv:math.DG/0002164
Geyer, Wulf-Dieter
Jede endliche Gruppe ist Automorphismengruppe einer endlichen Erweiterung K|Q
Arch. Math. 41 (1983), N2, 139-142
Availability: p7j4280673118j48.pdf; hardcopy
Ghanam, Ryad and Strugar, I. and Thompson, Gerard
Matrix representations for low dimensional Lie algebras
Extracta Math. 20 (2005), no. 2, 151--184
Ghanam, R. and Thompson, Gerard and Tonon, S.
Representations for six-dimensional nilpotent Lie algebras
Hadronic J. 29 (2006), no. 3, 299--317
Ghrist, Robert
Barcodes: The persistent topology of data
DOI: 10.1090/S0273-0979-07-01191-3
Bull. Amer. Math. Soc. 45 (2008), N1, 61-75
Description: A survey on peristent homology.
Availability: hardcopy (journal)
Giambruno, A. and Mishchenko, S. and Zaicev, M.
Polynomial identities on superalgebras and almost polynomial growth
Comm. Alg. 29 (2001), N9, 3787-3800
Availability: 100105975.pdf
Codimension growth of two-dimensional non-associative algebras
DOI: 10.1090/S0002-9939-07-08673-X
Proc. Amer. Math. Soc. 135 (2007), 3405-3415
Zentralblatt: pre05196049
Giambruno, Antonio and Regev, Amitai and Zaicev, Michail V.
Simple and semisimple Lie algebras and codimension growth
DOI: 10.1090/S0002-9947-99-02419-8
Trans. Am. Math. Soc. 352, No.4, 1935-1946 (2000)
Zentralblatt: 0970.17004
Description: p=0.
Availability: S0002-9947-99-02419-8.pdf
Giambruno, A. and Zaicev, M.
Codimension growth and minimal superalgebras
Trans. Amer. Math. Soc. 355 (2003), 5091-5117
Description: Supercommutative and Grassman envelopes, etc., in the spirit of Kemer.
Availability: S0002-9947-03-03360-9.ps
Polynomial Identities and Asymptotic Methods
AMS, 2005, 352 pp.
Availability: GiambrunoZaicevbook.pdf; google books
Gianni, Patrizia and Mora, Teo
Algebraic solution of systems of polynomial equations using Groebner bases
DOI: 10.1007/3-540-51082-6_83
Lecture Notes in Computer Science Volume 356/1989 Pages 247-257
Availability: 1989-algebraic.pdf
Gie, Pierre-Alexandre and Pinczon, Georges and Ushirobira, Rosane
Back to the Amitsur-Levitzki theorem: a super version for the orthosymplectic Lie superalgebra osp(1,2n)
DOI: 10.1023/B:MATH.0000017702.95884.c0
Lett. Math. Phys. 66 (2003), 141-155
Zentralblatt: 1051.17010 (Rutwig)
Description: Kostant's cohomological interpretation.
The Amitsur-Levitzki theorem for the orthosymplectic Lie superalgebra osp(1,2n)
J. Algebra Appl. 5 (2006), no. 3, 307--332
Zentralblatt: 1119.17009 (me)
Description: An expanded version of the previous paper.
Availability: hardcopy
Giesbrecht, M.
Fast computation of the Smith form of a sparse integer matrix
Computational Complexity Volume 10 Issue 1 (2001), pp 41-69
Abstract: We present a new probabilistic algorithm to compute the Smith normal form of a sparse integer matrix $ A \in {\Bbb Z}^{m \times n} $. The algorithm treats A as a "black box" - A is only used to compute matrix-vector products and we do not access individual entries in A directly. The algorithm requires about $ O(m^2 {\rm log} \parallel A \parallel) $ black box evaluations $ w \mapsto Aw\,{\rm mod}\,p $ for word-sized primes p and $ w \in {\Bbb Z}^{n \times 1}_p $, plus $ O(m^2 n\,{\rm log} \parallel A \parallel +\,m^3\,{\rm log^2} \parallel A \parallel) $ additional bit operations. For sparse matrices this represents a substantial improvement over previously known algorithms. The new algorithm suffers from no "fill-in" or intermediate value explosion, and uses very little additional space. We also present an asymptotically fast algorithm for dense matrices which requires about $ O(n \cdot {\rm MM}(m)\,{\rm log} \parallel A \parallel +\,m^3\,{\rm log^2} \parallel A \parallel) $ bit operations, where O(MM(m)) operations are sufficient to multiply two $ m \times m $ matrices over a field. Both algorithms are probabilistic of the Monte Carlo type - on any input they return the correct answer with a controllable, exponentially small probability of error.
Giglio, Beatrice and Riccomagno, Eva and Wynn, Henry P.
Grobner basis strategies in regression.
Journal of Applied Statistics; Sep2000, Vol. 27 Issue 7, p923
Description: Not very clear, though interesting.
Gil, Isabelle
Computation of the Jordan canonical from of the square matrix (Using the Axiom programming language)
ISSAC'92, ACM, 1992, 138-145
Availability: jordan.djvu
Gilbert, John R.
Predicting Structure in Sparse Matrix Computations
SIAM Journal on Matrix Analysis and Applications 15(1994), N1, 62-79
Abstract: Many sparse matrix algorithms---for example, solving a sparse system of linear equations---begin by predicting the nonzero structure of the output of a matrix computation from the nonzero structure of its input. This paper is a catalog of ways to predict nonzero structure. It contains known results for some problems, including various matrix factorizations, and new results for other problems, including some eigenvector computations.
Gilg, Marc
Low-dimensional filiform Lie superalgebras
Rev. Mat. Complut. 14(2001), no.2, 463-478
On Deformations of the Filiform Lie Superalgebra L_{n,m}
Communications in Algebra, Volume 32 , Issue 6, 2099 - 2115
Gille, Philippe and Pianzola, Arturo
Isotriviality of torsors over Laurent polynomial rings
DOI: 10.1016/j.crma.2005.10.013
Comptes Rendus 341 (2005), N12, 725-729
Description: Current Lie algebras.
Availability: sdarticle.pdf
Gille, Philippe and Szamuely, Tamás
Central Simple Algebras and Galois Cohomology
URL: http://www.cambridge.org/uk/0511223153 http://www.cambridge.org/uk/0521861039
Cambridge Univ. Press
Gilman, R.H.
On the definition of word hyperbolic groups
Math. Z., Published online: 1 February 2002
math.GR/0010123
Abstract: Formal languages based on multiplication tables of finitely generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups.
Gilmore, Robert
Lie Groups, Lie Algebras, and Some of Their Applications
Wiley, 1974
Description: Including contractions.
Availability: 1974-lie.djvu
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Gindikin, S.G.
Algebra logiki v zadachakh
Nauka, 1972 (in Russian)
Availability: Kolkhoz
Ginocchio, Maurice
Singular operations on algebras (generalized contractions)
Ann. Inst. H. Poincaré A 20 (1974), no. 1, 1-19
Description: Contractions of Lie algebras.
Availability: hardcopy
Ginot, Gre'gory
Homologie et mode`le minimal des alge`bres de Gerstenhaber
Preprint IRMA 2001-042
Ann. Math. Blaise Pascal 11 (2004), no. 1, 95--127
Description: Operadic approach.
Availability: 01042.ps
Ginot, Gregory and Halbout, Gilles
A formality theorem for Poisson manifolds
URL: http://www.ingentaconnect.com/content/klu/math/2003/00000066/F0020001/05125121 http://www-irma.u-strasbg.fr/~halbout/publications/formalite.ps
DOI: http://dx.doi.org/10.1023/B:MATH.0000017625.37702.7a
Lett. Math. Phys. 66 (2003), N1-2, 37-64
Abstract: Let M be a differential manifold. Using different methods, Kontsevich and Tamarkin have proved a formality theorem, which states the existence of a Lie homomorphism 'up to homotopy' between the Lie algebra of Hochschild cochains on C¥(M) and its cohomology (G(M, LTM), [-, -]S). Suppose M is a Poisson manifold equipped with a Poisson tensor p; then one can deduce from this theorem the existence of a star product * on C¥(M). In this Letter we prove that the formality theorem can be extended to a Lie (and even Gerstenhaber) homomorphism 'up to homotopy' between the Lie (resp. Gerstenhaber 'up to homtoptopy') algebra of Hochschild cochains on the deformed algebra (C¥(M), *) and the Poisson complex (G(M, LTM), [p, -]S). We will first recall Tamarkin's proof and see how the formality maps can be deduced from Etingof and Kazhdan's theorem using only homotopies formulas. The formality theorem for Poisson manifolds will then follow.
Ginzburg, Victor
Kvantovanoe i metod orbit
Matematicheskii Analiz. Vol. 22, VINITI, 1984, 37- (in Russian)
Description: Filtered deformations of polynomial algebras (related to "quantization")
Availability: mathem-analysis-22.{pdf.djvu} (whole volume)
Double derivations and cyclic homology
arXiv:math.KT/0505236
Abstract: We give a new construction of cyclic homology of an associative algebra that does not involve Connes' differential.
Lectures on noncommutative geometry
arXiv:math.AG/0506603
Ginzburg, Victor and Kaledin, Dmitry
Poisson deformations of symplectic quotient singularities
arXiv:math.AG/0212279
Adv. Math. 186 (2004), 1-57
Description: Poisson cohomology of a Poisson algebras as bicomplex (appendix). Involves Harrison complex. Kunneth formula for Poisson cohomology.
Ginzburg, V. and Kapranov, M
Koszul duality for operads
Duke M.J. 76 (1994), 203-272; Erratum: 80(1995), p.293
arXiv:0709.1228
Description: A famous paper everybody is refering to.
Availability: hardcopy; koszul.tex
Ginzburg, V. and Schechtman, V.
Screenings and a universal Lie-de Rham cocycle
AMS Transl. 181(1997), Kirillov's Seminar on Representation Theory
Ginzburg, Victor and Schedler, Travis
Moyal quantization and stable homology of necklace Lie algebras
arXiv:math.QA/0605704
Mosc. Math. J. 6 (2006), no. 3, 431--459
Description: To every quiver one associated a certain necklace Lie algebra, apparently generalizing situation with Kontsevich's graph homology and Hamiltonian Lie algebras.
Free products, cyclic homology, and the Gauss-Manin connection
arXiv:0803.3655
Description: A new approach to cyclic homology involving some variant od de Rham complex. Double derivations. Some deformations (where deformation parameter is non-commutative) which are described by H^2(A, A\otimes A).
Giraud, Jean
Cohomologie non abélienne
Springer, 1971
Availability: Kolkhoz
Giudici, M. and Li, C. and Potocnik, P. and Praeger, C.
Homogeneous factorizations of complete multipartite graphs
Research Report 2003/19, U. Western Australia
Availability: hardcopy
Giunashvili, Zakaria
Several cohomology algebras connected with the Poisson structure
Georgian Math. J. 5 (1998), N6, 513-520
Availability: v5n6-2.ps
Differential complex of Poisson manifold and distributions
arXiv:math-ph/0103038
Noncommutative geometry of phase space
arXiv:math-ph/0203027
Abstract: Geometric, algebraic and homologic structures related with Poisson structure on a smooth manifold.
The characteristic class of a Lie algebra ideal, contact structures and the Poisson algebra of basic functions
arXiv:math-ph/0205025, 30 pages
Description: Some cohomology classes associated with an ideal in a Lie algebra, a Poisson structure on the basic functions algebra of contact structure, its Poisson cohomology and geometric (pre)quantization are considered from the algebraic point of view.
Noncommutative symplectic geometry of the endomorphism algebra of a vector bundle
arXiv:math.SG/0212228
Description: General results about Poisson algebras, Poisson structures on matrix algebra. Description of Poisson brackets on associative algebras satisfying certain conditions (derivations which vanish on the center are inner, etc.) in terms of certain maps with cocycle-like equations resembling Hom-Lie algebras condition. Poisson structures on matrix algebra.
Givental, Alexander
Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture
alg-geom/9612001
Glass, A. M. W. and Riedel, Herbert H. J.
Growth sequences - a counterexample
DOI: 10.1007/BF01188049
Algebra Universalis Volume 21, Numbers 2-3 / June, 1985 Pages 143-145
Glassman, Neal D.
Cohomology of nonassociative algebras
BAMS 74 (1968), 590-594
Zentralblatt: 0279.18011
Description: "A cohomology theory of an arbitrary nonassociative algebra satisfying a set of identities"
Availability: hardcopy
Cohomology of nonassociative algebras
Pacific J. Math. 33 (1970), no. 3, 617-634
MR 0265419
Zentralblatt: 0217.34904
Availability: 1102976828.pdf; hardcopy
Cohomology of Jordan algebras
DOI: 10.1016/0021-8693(70)90072-4
J. Algebra 15 (1970), 167-194
MR 46#3585
Zentralblatt: 0217.35001
Availability: sdarictle-1.pdf
Glotko, N.V. and Kuz'minov, V.I.
On the Cohomology Sequence in a Semiabelian Category
Siberian Math. J. 43(2002), 28-35
Abstract: In a semiabelian category, a strictly exact sequence 0 -> A -> B -> C -> 0 of cochain complexes gives rise to the cohomology sequence ... -> H^n(A) -> H^n(B) -> H^n(C) -> H^n+1(A) -> ... We study conditions for exactness of the homology sequence at a given term.
Availability: fulltext.pdf
Gluck, David and Taylor, Brian D.
A new statistic for the 3x+1 problem
Proc. Amer. Math. Soc. 130 (2002), 1293-1301
Availability: S0002-9939-01-06305-5.ps
Gluskin, L.M.
Polugruppy
Algebra. Topologiya. 1962 (in Russian), 33-
Availability: algebra-top-1962.djvu (whole book)
Glutsyuk, Alexey
Instability of nondiscrete free subgroups in Lie groups
arXiv:math.DS/0409556
Description: Perturbations and approximation of free subgroups of Lie groups to/by non-free ones.
Gnedbaye, Allahtan Victor
Sur l'homologie des algèbres de Leibniz. Opérades des algèbres k-aires
Prebubl. IRMA, 1995, 045
MR 97k:17001
Suite spectrale d'une extension d'algèbres de Leibniz
C. R. Acad. Sci. Paris 324 (1997), No.12, 1327-1332
Zentralblatt: 0946.17007
Description: Analogue of the Hochschild-Serre spectral sequence for Leibniz algebras.
Leibniz homology of extended Lie algebras
K-Theory 13 (1998), No.2, 169-178
Zentralblatt: 0894.17002
Description: Leibniz cohomology of current Lie algebras, similar to Haddi's works.
Availability: w30470237173322m.pdf
Third homology groups of universal central extensions of a Lie algebra
ICTP Preprint No.IC98059, 1998
Afrika Mat. 10 (1999), 46-63
Zentralblatt: 1054.17003
Availability: Trieste preprints web site
Ope'rades, alge`bres de Leibniz et triples de Jordan
Preprint IRMA 2003-019
Habilitation, 2003
Abstract: Place'es dans le cadre de l'"alge`bre homologique non commutative" et de la "the'orie des ope`rades", mes activite's de recherches se scindent en deux parties inde'pendantes. La premie`re est consacre'e a` la ge'ne'ralisation de certaines proprie'te's classiques des alge`bres de Lie au cadre non commutatif des "alge`bres de Leibniz". J'y e'tudie les extensions centrales universelles, une version Leibniz de la suite spectrale de Hochschild-Serre, des produits tensoriels non abe'liens, et la notion d'"alge`bres de Leibniz e'tendues" (par un certain type de nouvelles alge`bres). La seconde partie s'occupe des ope'rades des alge`bres a` "ope'rations k-aires"(i.e., dont le produit porte sur k variables), avec une e'tude particulie`re des "triples de Jordan" qui sont des alge`bres ternaires (k = 3) issues de certaines relations alge`briques entre des ope'rateurs provenant de la "Me'canique Quantique".
Availability: IRMA preprints web site
Gnedbaye, Allahtan Victor and Wambst, Marc
J. Algebra 231 (2000), No.2, 744-757 Jordan triples and operads
Zentralblatt: 1002.18010
Description: Jordan triple systems in terms of operads.
Göbel, Rüdiger and Kegel, Otto H.
Group Algebras: Normal Subgroups and Ideals
DOI: 10.1007/s00032-007-0075-7
Milan Journal of Mathematics Volume 75, Number 1 / December, 2007 Pages 323-332
Abstract: Correspondence between the normal subgroups of the group G and some ideals of the group algebra FG.
Gobel, Rudiger and Paras, Agnes T.
Automorphisms of metabelian groups with trivial center
Illinois J.M. 42(1998), N2, 333-346
MR 99d:20057
Description: Every group is an outer automorphisms group of a certain metabelian group.
Realizing automorphism groups of metabelian groups
Abelian Groups and Modules (Bublin, 1998), Birkhauser, 1999, 309-317
MR 2001c:20079
Outer automorphism groups of metabelian groups
J. Pure Appl. Alg. 149(2000), N3, 251-266
MR 2001d:20034
Availability: gobel-paras-aut.pdf
Go"bel, Ru"diger and Paras, Agnes T. and Shelah, Saharon
Groups isomorphic to all their non-trivial normal subgroups
math.GR/0009088
Israel J Math. 129 (2002), 21-27
Gobel, Rudiger and Shelah, Saharon
Radicals and Plotkin's problem concerning geometrically equivalent groups
math.GR/0010303
Proc. Amer. Math. Soc. 130(2002), 673-674
Description: Quasiidentities, geometric equivalence.
Availability: hardcopy
How rigid are reduced products?
Journal of Pure and Applied Algebra Volume 202, Issues 1-3 , 1 November 2005, Pages 230-258
Availability: rigid.pdf
Godbillon, Claude
Geometrie Differentielle et Mecanique Analytique
Mir, 1973 (Russian translation from Hermann, Paris, 1969)
Availability: 1969-geometrie.djvu
Cohomologies d'algebres de Lie de champs de vecteurs formels
DOI: 10.1007/BFb0057302
Sem. Bourbaki 1972/1973, Exp. N 421, LNM 383 (1974), 69-87
Usp. Mat. Nauk 28 (1973), No.4, 139-151 (in Russian)
Zentralblatt: 0304.17004
Availability: godbillion.pdf
Goddard, P. and Kent, A. and Olive, D.
Virasoro algebras and coset space models.
Phys. Lett. B 152 (1985), no. 1-2, 88--92
MR 86m:81092
Description: Probably some interesting relation between affine nontwisted Kac-Moody and Virasoro algebras.
Gödel, K.
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
Dover, 1992; paperback, 72 pp.
Availability: hardcopy (book); Kolkhoz' obmennik
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Godement, R.
Topologie Algébrique et Théorie des Faisceaux
Novokuzneckii Fiz.-Mat. Inst., 2000 (Russian translation from French, 1958); paperback, small format, 316 pp.
Availability: hardcopy (book)
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Gokhberg, I.C. and Krein, M.G.
Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov v Hilbertovom prostranstve
Nauka, 1965 (in Russian)
Availability: Kolkhoz; absent on amazon
Teoriya Volterrovykh operatorov v Gilbertovom prostransyve i ee prilozheniya
Nauka, 1967 (in Russian)
Availability: Kolkhoz; absent on amazon
Goldberg, S.I.
Lie algebra extensions and enlargements of modules. I, II
Abstracts of talks presented to AMS meetings, BAMS January 1954, p. 62 and May 1954, p. 251
Description: Musing on the themes of first degree (relative) cohomology interpretation, Bockstein (connecting) homomorphisms, etc.
Availability: hardcopy
On the Euler characteristic of a Lie algebra
Amer. Math. Monthly 62 (1955), 239-240
Availability: goldberg.pdf; hardcopy
Curvature and Homology
revised ed., Dover, 1998; paperback
Availability: hardcopy (book); Kolkhoz
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Goldblatt, R.
Topoi. The Categorical Analysis of Logic
URL: http://cdl.library.cornell.edu/cgi-bin/cul.math/docviewer?did=Gold010 http://techlibrary.ru/books.htm
Mir, 1983 (Russian translation from North-Holland, 1979); hardcover, 486 pp.
Availability: hardcopy (book)
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Goldman, Jerry I.
On a class of nodal noncommutative Jordan algebras
TAMS 128 (1967), 176-183
Description: Their definiton resembles those of Poisson algebras (over divided power algebras, p>0). When they are Lie-admissibile.
Availability: 0-150.pdf
Goldman, M.A. and Krachkovskii, S.N.
Some perturbations of a closed linear operator
Doklady (?) circa 1964, 1243-1245
Availability: hardcopy
Goldman, William M. and Millson, Jon J.
The deformation theory of representations of fundamental groups of compact Kahler manifolds
BAMS 18 (1988), N2, 153-158
Description: The kahler-manifolds deformation-theoretic business linked with some generic algebraic statements formulated in terms of differentiall graded Lie algebras and showing, roughly, that deformations are the same provided cohomology are the same.
Availability: hardcopy (journal)
The deformation theory of representations of fundamental groups of compact Kahler manifolds
Publ. Math. IHES 67 (1988), 43-96
Description: Could be interesting in light of "cohomology of a sum of Lie brackets" constructions.
Availability: hardcopy
Goldschmidt, D.M.
Group Characters, Symmetric Functions, and the Hecke Algebra
URL: http://www.ams.org/online_bks/ulect4/ http://ef12517-2.tu-sofia.bg/Desislav Todorov/Frames/Books/Mathematics/Algebra/
AMS
Availability: Kolkhoz; amazon
Golenishcheva-Kutuzova, Maria
Higher-dimensional generalizations of affine Kac-Moody and Virasoro conformal Lie algebras
DOI: 10.1007/s00220-005-1502-7
arXiv:math.QA/0411491
Comm. Math. Phys. 263 (2006), N3, 583-610
Golenichsheva-Kutuzova, M.I. and Lebedev, D.R.
Z-graded trigonometric Lie subalgebras in A^_\infty, B^_\infty, C^_\infty, and D^_\infty anf their vertex operator representations
Funct. Anal. Prilozh. 27 (1993), N1, 12-24
Description: Some families of algebras are defined and their interplay with others (Vershik, Virasoro-like, Kac-Moody, Poisson). Central extensions.
Availability: hardcopy
Golic, Jovan Dj.
Vectorial Boolean Functions and Induced Algebraic Equations
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY 2006
Description: Interrelationship between boolean functions and polynomial equations, Groebner bases.
Availability: 01580793.pdf
Golod, P.I. and Klimyk, A.Yu.
Matematicheskie osnovy teorii simmetrii
R&C Dynamics, 2001 (in Russian); hardcover, 528 pp.
Availability: hardcopy; Kolkhoz
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Golod, P.I. and Skrypnyk, T.V.
Anisotropic quasigraded Lie algebras on hyperelliptic curves and integrable Hamiltonian systems (Ukrainian)
Nauk. Zap., Kyi"v 18, 20-25 (2000)
Zentralblatt: 0974.17036
Description: Central extensons.
Golod, E.S.
O nekotorykh problemakh Bernsaidovskogo tipa (in Russian)
Proc. ICM 1966, Moscow, 264-
Availability: Kolkhoz (whole book)
Standard bases and homology
DOI: 10.1007/BFb0082019
LNM 1352 (1988), 88-95
Zentralblatt: 657.13013
Description: Ufnarovskii: homological interpretation of the composion (=diamond) lemma.
Availability: hardcopy
Golod, P.
Hamiltonian systems connected with anisotropic affine Lie algebras and higher Landau-Lifshits equations (Russian)
Dokl. Akad. Nauk Ukr. SSR, Ser. A 1984, No.5, 6-8
Zentralblatt: 0542.58010
Description: Deformation of affine Lie algebra based on sl(2).
A deformation of the affine Lie algebra $A_1^{(1)}$ and hamiltonian systems on the orbits of its subalgebras
Group-theoretical methods in physics, Moscow, Nauka, 1986, pp. 368--376
Description: Advertised by Leites as deformation of "loop algebra".
Golub, Gene H.
Milestones in Matrix Computation: Selected Works of Gene H. Golub, with Commentaries
Oxford Univ. Press, 2007
Availability: 2007-milestones.djvu
Golub, G.H. and Van Loan, C.F.
Matrix Computations
3rd ed., The Johns Hopkins U. Press, 1996
Availability: hardcopy (book; Russian translation from the 2nd ed.)
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Golub, Gene H. and Vorst, Henk A. van der
Eigenvalue computation in the 20th century
J. Comput. Appl. Math. 123(2000), N1-2, 35-65
Abstract: This paper sketches the main research developments in the area of computational methods for eigenvalue problems during the 20th century. The earliest of such methods dates back to work of Jacobi in the middle of the 19th century. Since computing eigenvalues and vectors is essentially more complicated than solving linear systems, it is not surprising that highly significant developments in this area started with the introduction of electronic computers around 1950. In the early decades of this century, however, important theoretical developments had been made from which computational techniques could grow. Research in this area of numerical linear algebra is very active, since there is a heavy demand for solving complicated problems associated with stability and perturbation analysis for practical applications. For standard problems, powerful tools are available, but there still remain many open problems. It is the intention of this contribution to sketch the main developments of this century, especially as they relate to one another, and to give an impression of the state of the art at the turn of our century.
Golubchik, I.Z. and Sokolov, V.V.
Integrable systems generated by a constant solution of the Yang-Baxter equation
DOI: 10.1007/BF02509622
Funct. Anal. Appl. 30 (1996), N4, 275-277
Description: Some interesting general facts about R-matrix (probably well-known, with further references)
Availability: 1996-integrable.pdf
Factorization of the loop algebra and integrable toplike Systems
DOI: 10.1023/B:TAMP.0000043852.90703.0b
Theor. Math. Phys. 141 (2004), N1, 1329-1347
Description: "Factorization" means (some specific) decomposition into sum of subalgebras.
Compatible Lie brackets and the Yang-Baxter equation
DOI: 10.1007/s11232-006-0016-6
Theor. Math. Phys. 146 (2006), N2, 159-169
Abstract: We show that any pair of compatible Lie brackets with a common invariant form produces a nonconstant solution of the classical Yang-Baxter equation. We describe the corresponding Poisson brackets, Manin triples, and Lie bialgebras. It turns out that all bialgebras associated with the solutions found by Belavin and Drinfeld are isomorphic to some bialgebras generated by our solutions. For any compatible pair, we construct a double with a common invariant form and find the corresponding solution of the quantum Yang-Baxter equation for this double.
Golubeva, V.A. and Leksin, V.P.
Rigidity theorems for multiparametric deformations of the universal enveloping algebras.
Complex analysis and representation theory, 3, VINITI
J. Math. Sci. 108 (2002), no. 3, 420--431.
Rigidity theorems for multiparametric deformations of algebraic structures, associated with the Knizhnik-Zamolodchikov equations
J. Dyn. Control Syst. 13 (2007), no. 2, 161--171
Golubitsky, Martin and Rothschild, Bruce
Primitive subalgebras of exceptional Lie algebras
DOI: 10.1090/S0002-9904-1971-12828-8
Bull. Amer. Math. Soc. 77 (1971), 983-986
Golubkov, Artem Yu.
Prime radicals of Chevalley groups over commutative rings
J. Math. Sci. 102 (2000), N6, 4581-
Description: A normal subgroup P of a group G is called prime, if the centralizer of each nontrivial normal subgroup is {1} in G/P. The interscetion of all prime subgroups is called a prime radical of a group.
Availability: fulltext-2.pdf
The prime radical of the special Lie algebras and the elementary Chevalley groups
Comm. Algebra 32 (2004), N5, 1649-1683
Abstract: Linear groups over rational associative algebra with unity.
Gomez, Xavier
Classification of three-dimensional Lie bialgebras
DOI: 10.1063/1.533385
J. Math. Phys. -- July 2000 -- Volume 41, Issue 7, pp. 4939-4956
Go'mez Ambrosi, C. and Laliena, Jesu's and Shestakov, I.P.
On the Lie Structure of the Skew Elements of a Prime Superalgebra with Superinvolution
Comm. Algebra 28(2000), N7, 3277-3291
MR 2001g:17007
Gomez-Ambrosi, Carlos and Shestakov, Ivan P.
On the Lie structure of the skew elements of a simple superalgebra with superinvolution
DOI: 10.1006/jabr.1998.7452
J. Algebra 208 (1998), 43-71
Go'mez, J.R. and Jimene'z-Mercha'n, A. and Khakimdjanov, Y.
Classifying filiform Lie algebras with Mathematica
Kera"nen, Veikko (ed.) et al., Innovation in mathematics. Proceedings of the 2nd international $Mathematica$ symposium, Rovaniemi, Finland, July 1997. Southampton: CMP, Computational Mechanics Publications. 169-176 (1997)
Zentralblatt: pre02145163
Gomez, J.R. and Khakimdjanov, Yu. and Navarro, R.M.
Some problems concerning to nilpotent Lie superalgebras
DOI: 10.1016/j.geomphys.2004.01.003
J. Geom. Phys. 51 (2004), N4, 472-485
Infinitesimal deformations of the Lie superalgebra Ln,m
DOI: 10.1016/j.geomphys.2008.02.005
Journal of Geometry and Physics Volume 58, Issue 7, July 2008, Pages 849-859
Gomez, Xavier and Mazorchuk, Volodymyr
ON AN ANALOGUE OF BGG-RECIPROCITY
Communications in Algebra, Volume 29 , Issue 12 (2001), 5329 - 5334
Description: projectives in O category, etc.; sl(2) example.
Availability: bgg.pdf
Goncalves, Jairo Z.
Free groups in subnormal subgroups and the residual nilpotence of the group of units of group rings
Canad. Math. Bull. 27 (1984), N3, 365-370
Description: Theorem 2.1: Finite-dimensional division rings contain free subgroups of rank two.
Availability: google print; 1984-free.tar
Gonçalves, Daciberg Lima and Guaschi, John
The quaternion group as a subgroup of the sphere braid groups
DOI: 10.1112/blms/bdl041
Bull. London Math. Soc. 39 (2007), N2, 232-234
Description: The quaternion group of order 8 is realised as a subgroup of the sphere braid group B_n(S^2) if and only if n is even.
Availability: hardcopy
Gonçalves, Jairo Z. and Mandel, Arnaldo
Are there free groups in division rings?
DOI: 10.1007/BF02772670
Israel J. Math. 53 (1986), N1, 69-80
Goncalves, J.Z. and Shirvani, M.
On free group algebras in division rings with uncountable center
URL: http://links.jstor.org/sici?sici=0002-9939(199603)124%3A3%3C685%3AOFGAID%3E2.0.CO%3B2-R http://www.ams.org/proc/1996-124-03/S0002-9939-96-03032-8/home.html
Proc. AMS 124 (1996), No.3, 685-687
Description: Over uncountable field, if a division ring contains a free algebra of rank 2 then it contains a free group algebra.
Free Groups in Central Simple Algebras without Tits' Theorem
DOI: 10.1080/00927870802068292
Communications in Algebra, Volume 36, Issue 8 August 2008 , pages 3113 - 3121
Availability: 901796735.pdf
Goncharov, A.B.
Infinitesimal structures that are connected with Hermitian symmetric spaces
Funkt. Anal. Prilozh. 15 (1981), no. 3, 83--84
MR 83k:32046
Availability: hardcopy
Generalized-conformal structures on varieties.
Problems in group theory and homological algebra (Yaroslavl) 138 (1983), 99--111
MR 87a:53064
Description: Structure functions
Generalized conformal structures on manifolds.
Selecta Math. Soviet. 6 (1987), no. 4, 307--340
(Leites') Seminar on Supermanifolds, Stockholm U., 11/1987-15, p.16-70
MR 89e:53050
Description: Structure functions associated to CHSS.
Availability: hardcopy
Goncharov, M. E.
The classical Yang-Baxter equation on alternative algebras: The alternative D-bialgebra structure on Cayley-Dickson matrix algebras
DOI: 10.1007/s11202-007-0083-4
Siberian Mathematical Journal Volume 48, Number 5 / September, 2007 Pages 809-823
Goncharova, L.V.
O cohomologiyakh algebr Lie verktornykh polei na algebraicheskikh krivykh
UMN 1(1972), N1, 243-244
Availability: CWI
Cohomologii algebr Lie formalnykh vektornykh polei na pryamoi
UMN circa 1972, 231-232
Availability: hardcopy
Gong, Ming-Peng
Classification of nilpotent Lie algebras of dimension 7 (over algebraically closed fields and R)
URL: http://etd.uwaterloo.ca/etd/mpgong1998.pdf http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0009/NQ30613.pdf
PhD Thesis, U. of Waterloo, 1998
Gonshor, Harry
Multi-algebra duplication
DOI: 10.1007/BF00275502
J. Math. Biol. 25 (1987), 677-683
Zentralblatt: 0658.92015
Availability: 1987-multi.pdf
Gonzalez, S. and Martinez, C.
Lie mutation of an associative algebra
Algebras Groups Geom. 2 (1985), 129-138
MR 88f:17019
Zentralblatt: 0586.17012
Availability: hardcopy
Goodearl, K.R. and Menal, P.
Free and residually artinian regular rings
J. Alg. 156(1993), 407-432
Description: Proposition 2.1: every countable-dimensional associative algebra can be embedded into algebra of \omega x \omega matrices which are simultaneously row-finite and column-finite.
Goodwillie, Thomas
Cyclic homology, derivations, and the free loopspace
Preprint, Harvard Univ.
Availability: hardcopy
On the general linear group and Hochschild homology
DOI: 10.2307/1971179
Ann. Math. 121 (1985), no. 2, 383--407; correction: 124 (1986), no. 3, 627--628
MR 86i:18013; correction: MR 87k:18014
Description: Cohomology of gl(A) with coefficients in M(B). Relations to homology of linear group GL(A).
Availability: 1985-general.pdf
Goralcik, P. and Koubek, V.
Pseudovarieties and pseudotheories
Finite algebra and multiple-valued logic, Colloq. Math. Soc. Ja'nos Bolyai 28, North-Holland, 1981, 301--324
MR 83c:08010
Zentralblatt: 0488.08004
Description: Birkhoff-like characterization of pseudovarieties.
Gorbatsevich, V.V.
On contractions and degeneracy of finite-dimensional algebras
Sov. Math. (Izv. VUZ) 35 (1991), N10, 19-27
Description: Hierarchy on the space of all n-dimesnional algebras: algebra is on nth level if it is contractible at n "elementary" steps to a trivial abelian algebra.
Availability: hardcopy
Antinilpotent Lie algebras
DOI: 10.1007/s11006-005-0180-2
Math. Notes 78 (2005), N5-6, 749-756
Description: Lie algebras, all whose nilpotent subalgebras are abelian, mainly over R.
Invariant intrinsic Finsler metrics on homogeneous spaces and strong subalgebras of Lie algebras
DOI: 10.1007/s11202-008-0004-1
Siber. Math. J. 49 (2008), N1, 36-47
Description: Subalgebra S of a Lie algebra L is called strong if any S-invariant subspace of L containing S is a subalgebra of L. Characterization of strong subalgebras in finite-dim. Lie algebras, p=0.
Gorbatsevich, V.V. and Onishchik, A.L. and Vinberg, E.B.
Lie groups and Lie algebras III. Structure of Lie groups and Lie algebras
URL: http://ignat.livejournal.com/24986.html http://homepages.cwi.nl/~mich/reviews/AAA_1011.html
Encyclopaedia of Mathematical Sciences, Vol. 41, Springer, 1994
Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Fundam. Napravleniya 41, VINITI, 1990
Zentralblatt: 0733.22003
Availability: lie-groups-lie-algebras-3.djvu; google books
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google books
Gorbunov, Victor A.
Structure of lattices of varieties and lattices of quasivarieties: Similarity and difference. I
DOI: 10.1007/BF00750161
Algebra and Logic Volume 34, Number 2 / March, 1995 Pages 73-86
Availability: 1995-structure.pdf
Algebraic Theory of Quasivarieties
Novosibirsk, 1999 (in Russian)
Availability: Kolkhoz; 1999-algebraic.djvu
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Isaev, A.P. and Ogievetskii, O.V.
The BRST operator for quantum Lie algebras: a connection with the bar complex
arXiv:0711.4133
Theor. Math. Phys. 139 No. 1 (2004) 473
Gorchakov, Yu.M.
Gruppy s konechnymi klassami sopryazhennykh elementov
Nauka, 1978, 119 pp.
Zentralblatt: 0496.20025
Gorchinskiy, S.O. and Parshin, A.N.
Adelic Lefschetz formula for the action of a one-dimensional torus
math.AG/0408058
Description: Lefschetz formula resembles Euler-Poincare characteristics. Some other similar formulas from linear algebra and algebraic geometry.
Gordeev, Nikolai and Grunewald, Fritz and Kunyavskii, Boris and Plotkin, Eugene
A commutator description of the solvable radical of a finite group
GROUPS, GEOMETRY, AND DYNAMICS Volume 2, Issue 1, 2008, pp. 85-120
Gordeev, Nikolai L. and Popov, Vladimir L.
Automorphism groups of finite dimensional simple algebras
arXiv:math.RA/0404009
Ann. Math. 158 (2003), no. 3, 1041--1065
Abstract: Roughly, every liner algebraic group over an algebraically closed field, and each finite group, is isomorphic to an automorphism group of a certain simple (nonassociative) algebra.
Availability: hardcopy
Gordeev, Nicolai and Rehmann, Ulf
On multicommutators for simple algebraic groups
URL: http://www.mathematik.uni-bielefeld.de/LAG/man/056.html http://www.mathematik.uni-bielefeld.de/sfb343/preprints/index00.html
DOI: 10.1006/jabr.2001.8929
J. Alg. 245 (2001), 275-296
Description: There are several examples of groups for which any pair of commutators can be written such that both of them have a common entry, and one can look for a similar property for $n$-tuples of commutators. We here answer, for simple algebraic groups over any field, the weaker question, under which condition the set of $n$-tuples of commutators with one common entry is Zariski dense in the set of all $n$-tuples of commutators. Surprisingly, there is a uniform bound on $n$ in terms of the so called Coxeter number of $G$ in order to answer the question positively. An analogoue result is proved for Lie algebras of simple and simply connected algebraic groups.
Availability: hardcopy
Gordon, S.R.
Associators in simple algebras
Pacific J.M. 51(1974), N1, 131-141
Description: Every element with trace zero in Cayley-Dickson algebra may be represented as a commutator.
Gordon, Iain and Premet, Alexander
Block representation type of reduced enveloping algebras
Trans. Am. Math. Soc. 354, No.4, 1549-1581 (2002)
Zentralblatt: 1054.20025
Availability: Premet's homepage; block3.ps
Goresky, Mark and Kottwitz, Robert and MacPherson, Robert
Equivariant cohomology, Koszul duality, and the localization theorem
Preprint, circa 1996, 53 pp.
Availability: hardcopy
Gorinov, A.G.
On cohomologies of double complexes
Mosc. Univ. Math. Bull. 52 (1997), No.5, 40-41
Vestn. Mosk. Univ., Ser. I 1997, No.5, 54-56
Zentralblatt: 0906.55014
Description: Let C^** be a double complex and C^* its diagonal complex. For any possible definition of differential d = ad_1 + bd_2, the obtained complexes are isomorphic.
Availability: hardcopy
Goss, D.
Basic Structures of Function Field Arithmetic
Springer, 2nd printing, 1998; paperback, 424 pp.
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Goto, Morikuni
On algebraic Lie algebras
J. Math. Soc. Japan 1 (1948), N1, 29-45
Description: A matrix Lie algebra L is called algebraic, if for every matrix A belonging to L all matrices having the same set of invariants as A, also belong to L.
Availability: hardcopy
Goto, M. and Grosshans, F.
Semisimple Lie Algebras
URL: http://techlibrary.ru/books.htm http://ignat.livejournal.com/24986.html
Novokuzneckii Fiz.-Mat. Inst., 1998 (Russian translation from English, 1978); paperback, small format, 336 pp.
Availability: hardcopy; Kolkhoz
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Goto, S. and Nishida, K.
The Cohen-Macauley and Gorenstein Rees Algebras Associated to Filtrations
Memoirs AMS, No. 526, 1994; paperback, 134 pp.
Availability: hardcopy (book)
Gotsman, Craig and Toledo, Sivan
On the computation of null spaces of sparse rectangular matrices
Availability: hardcopy
Gotz, Gerhard and Quella, Thomas and Schomerus, Volker
Representation theory of sl(2|1)
DOI: 10.1016/j.jalgebra.2007.03.012
arXiv:hep-th/0504234
J. Algebra 312 (2007), N2, 829-848
Description: Full description of irreducibles. Decompositions of their tensor products.
Gould, Henry Wadsworth
Combinatorial Identities: A Standardized Set of Tables Listing 500 Binomial Coefficient Summations
Morgantown, WV, 1972. 106 p.
Gould, M. D.
A trace formula for semi-simple Lie algebras
Annales de l'institut Henri Poincaré (A) Physique théorique, 32 no. 3 (1980), p. 203-219
Description: Decomposition of tensor product of irreducibles, including Klimuk's formula.
Goursat, E.
Lecons sur l'intégration des équations aux dérivées partielles du premier ordre
Hermann, Paris, 1891
Availability: hardcopy (book)
Gover, A. Rod and Slovak, Jan
Invariant local twistor calculus for quaternionic structures and related geometries
J. Geom. Phys. 32(1999), No.1, 14-56
Zentralblatt: 0981.53031
Description: On p. 37 appears a graph of Young diagrams resembling mine.
Availability: JGPver.ps
Govorov, V E
Algebras of homological dimension 1
DOI: 10.1070/SM1983v044n01ABEH000953
Math USSR Sbornik 44 (1983), N1, 97-107
MR 632491
Zentralblatt: 0483.16025
Description: Associative algebras and groups. An associated graded algebra of an algebra of homological deimension 1 is free.
Gow, Rod
Commutators in finite simple groups of Lie type.
Bull. London Math. Soc. 32(2000), 311-315
Abstract: Using properties of the Steinberg character, we obtain a congruence modulo p for the number of ways in which a p-regular element may be expressed as a commutator in a finite simple group G of Lie type of characteristic p. This congruence shows that such an element is a commutator in G. We also show that if K and L are conjugacy classes of G consisting of elements whose centralizers have order relatively prime to p, then any p-regular element of G is expressible as the product of an element of K and an element of L.
Goze, Michel
Algèbres de Lie modeles et déformations
C. R. Acad. Sci. Paris 292 (1981), 813-815
Zentralblatt: 0472.53025
Description: Classification of Lie algebars "up to contraction".
Availability: hardcopy
Mode`les d'alge`bres de Lie frobeniusiennes
C. R. A. S. Paris 293 (1981), 425-427
Zentralblatt: 0483.53012
Description: Classification of Frobenius Lie algebras up to contraction.
Availability: hardcopy
Perturbations sur une variété algébrique; application à l'étude locale de la variété des lois d'algèbres de Lie sur C^n
C. R. Acad. Sci. Paris 295 (1982), 583-586
Zentralbla