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[NOAUTHORS]
Vaintrob, A.Yu.
Lie algebroids and homological vector fields
UMN 52(1997), N2, 161-163
Rus. Math. Surv. 52(1997), N2
Description: Deformation theory for Lie algebroids analogous to those for Lie algebras.
Availability: vai05202.ps; LieAlgebroids(UMN52,97).{tex,dvi}
Darboux theorem and equivariant Morse lemma
Manuscript
Availability: MorseJGeomPhys.{tex,dvi}
Vais, A.Ya.
Special varieties of Lie algebras
DOI: 10.1007/BF01980605
Algebra and Logic 28 (1989), no.1, 17-24
MR 91e:17025
Description: p=0. A Lie algebra is called normal if its associative algebra generated by ad(L) is PI. A variety is called special, if it is generated by a normal Lie algebra. Theorem 1: Any special variety M of Lie algebras is generated by the Grassmann envelope of a finitely generated M-superalgebra. Theorem 2: Let M be a special variety of Lie algebras which does not contain sl(2). Then M is a solvable variety. The method is to follow a Kemer approach for Wedderburn-like structure theory of varieties of associative algebras (though results in this case are much weaker).
Availability: hardcopy
Vaisman, Izu
Remarks on the Lichnerowicz-Poisson cohomology
Ann. Inst. Fourier 40 (1990), no.4, 951-963
Lectures on the geometry of Poisson manifolds
Birkhäuser, 1994, 205 p.
Zentralblatt: 0810.53019
Description: Dirac brackets, Lie-Poisson structures.
Vallette, Bruno
Dualite de Koszul des PROPs
arXiv:math.QA/0405057
Ph. D. Thesis
Abstract: In this thesis, we generalize the Koszul duality for associative algebras and operads to PROPs. The operads are algebraic objects that represent the operations with multiple inputs but only one output acting on a certain type of algebras. A PROP models the operations with multiple inputs and multiple outputs acting on algebraic structures like bialgebras and Lie bialgebras. We also give a construction of the free monoid (for a monoidal product non-necessarily bilinear). We generalize the Poincare series of operads to PROPs and we prove a functional equation for Poincare series of Koszul PROPs.
Van Bommel, Jos
Rumors
J. Finance LVIII(2003), N4, 1499-
Availability: hardcopy
Van Daele, A.
On a certain class of semi-simple subalgebras of a semi-simple Lie algebra
Annales de l'institut Henri Poincaré (A) Physique théorique, 13 no. 3 (1970), p. 195-213
MR 271175
Zentralblatt: 0206.32201
Van der Linden, Tim
Homology and homotopy in semi-abelian categories
math.CT/0607100
Ph.D. Thesis, Vrije Universiteit Brussel
Description: Unification of nonabelian cohomology theories, including those of Lie algebras, in the language of semi-ableian categories.
Van Oystaeyen, Freddy
Algebraic Geometry for Associative Algebras
Marcel Dekker, 2000
Availability: Kolkhoz
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Vanden Eynden, Charles
Applications of a product identity to sums of squares and partitions
Amer. Math. Monthly 94(1987), No.7, 652-656
Availability: 3.pdf
Vapnik, Vladimir N.
Statistical Learning Theory
Wiley, 1998
Availability: 1998-statistical.djvu
The Nature of Statistical Learning Theory
Springer, 2nd ed., 2000
Availability: 2000-nature.djvu
Varadarajan, V.S.
On the ring of invariant polynomials on a semisimple Lie algebra
AJM 90 (1968), N1, 308-317
Availability: varadarajan.pdf
Lie Groups, Lie Algebras and Their Representations
Springer, 1984
Availability: Kolkhoz; VRII 512.55 Var
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Supersymmetry for Mathematicians: An Introduction
AMS, 2004, 300 pp.
Description: Introduction to super linear algebra and supermanifolds. Super-Brauer group.
Availability: 31$
Varagnolo, M. and Vasserot, E.
Double-loop algebras and the Fock space.
q-alg/9612035
Invent. Math.
Description: "central extension of a current algebra over a quantum torus" involved
Varea, Vicente R.
Lie algebras none of whose Engel subalgebras are in intermediate position
DOI: 10.1080/00927878308823551
Comm. Algebra 15 (1983), N12, 2529-2543
Availability: 780150030_content.pdf
Lie algebras whose maximal subalgebras are modular
Proc. Roy. Soc. Edinb. Sec. A 94 (1983)
On Lie algebras in which the relation of being an ideal is transitive
DOI: 10.1080/00927878508823208
Comm. Algebra 13 (1985), N5, 1135-1150
Existence of ad-nilpotent elements and simple Lie algebras with subalgebras of codimension one
DOI: 10.2307/2046980
PAMS 104 (1988), No.2, 363-368
Description: 1. The following is equivalent: (i) Any Lie algebra over F contains ad-nilpotent element (ii) There are no simple Lie algebras over F having only abelian subalgebras 2. Description of simple Lie algebras with a subalgebra of codimension 1. p>2.
Availability: 0-150.pdf
Lie algebras with anisotropic Engel subalgebras
J. Alg. 121 (1989), N1, 81-98
Zentralblatt: 0666.17003
Description: Lie algebras in which each element is either nilpotent or semisimple.
Modular subalgebras, quasi-ideals and inner ideals in Lie algebras of prime characteristic
Comm. Algebra 21 (1993), no.11, 4195-4218
MR 94g:17037
Availability: CWI
Supersimple and upper semimodular Lie algebras
DOI: 10.1080/00927879508825347
Comm. Alg. 23 (1995), N6, 23232330
Description: All subalgebras are simple. "The existence of [a Lie algebra all whose proper subalgebras are 1-dimensional] of dimension greater than three is an interesting open problem".
Availability: 780098735.pdf
Lie algebras all of whose proper subalgebras are solvable
Comm. Alg. 23 (1995), N9, 3245-3267
Description: Over alg. cl., p>0 (extensions of sl(2)).
Availability: minimal_nonsolv__final.pdf; hardcopy
Varea, V. R. and Varea, J. J.
Groups of automorphisms of Lie algebras such that the fixed-point subalgebra of each non-identity element is solvable
J. Algebra 277 (2004), no. 1, 129--156
Description: p=0.
On automorphisms and derivations of a Lie algebra
Algebra Colloq. 13 (2006), N1, 119-132
Description: In terms of Levi decomposition.
Availability: 19267507.pdf
Vaserstein, L N (=Vasershtein)
FOUNDATIONS OF ALGEBRAIC K -THEORY
RUSS MATH SURV, 1976, 31 (4), 89-156
Abstract: The fundamental concepts of (general) algebraic K-theory are expounded and it is proved that the higher K-functors of Volodin, Quillen, Swan and Gersten are the same.
Vaserstein, L.N. and Wheland, E.
Commutators and companion matrices over rings of stable rank 1
Linear Algebra and its Applications Volume 142 , December 1990, Pages 263-277
Abstract: We consider the group GLnA of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition. We prove that every matrix is similar to the product of a lower and upper triangular matrix, and that it is also the product of two matrices each similar to a companion matrix. We use this to show that, when n3 and A is commutative, every matrix in SLnA is the product of two commutators.
Vasilovskii, S.Yu.
The basis of identities of a three-dimensional simple Lie algebra over an infinite field
Alg. and Log. 28(1989), N5, 355-368
MR 92a:17007
Description: Previously known result for p=0 (Razmyslov & Filippov) proved for p \ne 2.
Availability: CWI
Vaughan-Lee, Michael
Superalgebras and dimensions of algebras
DOI: 10.1142/S0218196798000065
Internat. J. Algebra Comput. 8 (1998), no. 1, 97--125
MR 99a:17014
Zentralblatt: 0923.16023
Description: Power of superalgebra technique for calculations in relatively free algebras is demonstrated.
Availability: S0218196798000065.pdf
Simple Lie algebras of low dimension over GF(2)
LMS J. Comput. Math. 9 (2006), 174--192
Vavilov, Nikolai A.
Do it yourself structure constants for Lie algebras of types E_l
DOI: 10.1023/B:JOTH.0000017882.04464.97
Zapiski Nauchn. Sem. POMI 281 (2001), 60-104
J. Math. Sci. 120 (2004), N4, 1513-1548
MR 2002k:17022 (Rutwig)
Description: Explicit construction of bases for simple Lie algs E_6, E_7, E_8 using Mathematica. General reasonings about simple Lie algebras (Chevalley base, roots etc.)
Availability: p060.ps; hardcopy
How is one to view the signs of structure constants?
Algebra i Analiz 19 (2007), no.4, 34--68
Konkretnaya teoriya grupp
Description: Draft of a textbook. Very interesting and provocative.
Vavilov, N.A. and Gavrilovich, M.R. and Nikolenko, S.I.
Structure of Chevalley groups: the proof from the Book
Zap. Nauchn. Sem. POMI 330 (2006), 36-76
J. Math. Sci., New York 140, No. 5, 626-645 (2006)
Zentralblatt: pre05029496
Description: Structure of Chevalley groups over commutative rings.
Vavilov, N.A. and Petrov, V.A.
Variations on a theme of Higman
DOI: 10.1023/B:JOTH.0000042306.32825.6a
Zapiski Nauchnyh Seminarov POMI 289 (2002), 57-
J. Math. Sci. 124 (2004), 4708-4710
MR 2003i:20083
Description: H^1(st(n,R)) over commutative ring R.
Availability: p057.ps
Velaacutesquez, Rauacutel and Felipe, Raul
Quasi-Jordan Algebras
DOI: 10.1080/00927870701865996
Communications in Algebra, Volume 36, Issue 4 April 2008 , pages 1580 - 1602
Description: Kostrikin and Benkart-Isaacs results about element with (adx)^3 = 0 are extended to Leibniz algebras.
Venkov, B.B.
Some homological properties of Burnside groups
J. Math. Sci. 6(1976), N3, 239-252
Zapiski Nauchn. Sem. LOMI 31(1973), 38-54
Availability: h5166011717464w0.pdf
Verbitsky, Misha
Action of the Lie algebra of SO(5) on the cohomology of a hyper-Kahler manifold
Funct. Anal. Prilozh. 24 (1990), N3, 70-71
Funct. Anal. Appl. 24 (1991), N3, 229-230
Mirror symmetry for hyperkaehler manifolds
Preprint, 1995, 64 pp.
Availability: hardcopy
Quaternionic Dolbeault complex and vanishing theorems on hyperkahler manifolds
DOI: 10.1112/S0010437X07002746
arXiv:math/0604303
Compositio Mathematica (2007), 143:1576-1592
Description: Some bi-like-complexes resembling (a simplified version of) "complex ariging from Young diagrams decompositions" (only symmetric and skew-symmetric terms are present).
Vereshchagin, N.K. and Shen, A.
Vychislimye funkcii
MCCME, Moscow, 1999 (in Russian); softcover, 173 pp.
Availability: hardcopy (book)
Vergne, Michele
Cohomologie des algebres de Lie nilpotentes. Application a l'etude de la variete des algebres de Lie nilpotentes
Bull. Soc. Math. France 98(1970), 81-116
MR 44#6797
Zentralblatt: 0244.17011
Description: Chap. 5: Cohomology in variety of nilpotent Lie algebras.
La structure de Poisson sur l'algebre symetrique d'une algebre de Lie nilpotente
Bull. Soc. Math. France 100 (1972), 301-335
MR 52#657
Zentralblatt: 0256.17002
Quantification geometrique et reduction symplectique
Sem. Bourbaki 2000/2001, No.888
Availability: sem-bourbaki.pdf
Geometric quantization and cohomology
Description: A survey.
Availability: quantization.pdf
Verma, Daya-Nand
Structure of certain induced representations of complex semisimple Lie algebras
BAMS, circa 1967
Description: what is subsequently was called Verma modules is introduced.
Availability: hardcopy
Vershik, A.M.
A new class of infinite-dimensional Lie algebras (continumm Lie algebras) and associated nonlinear systems
Lect. Notes Phys. 375 (1991), 162-170
MR 92h:17024
On classification of Z-graded Lie algebras of constant growth which have algebra C[h] as Cartan subalgebra
LNM 1510 (1992), 395
MR 93d:00038
Lie algebras generated by dynamical systems
St. Petersburg Math. J. 4 (1993), N6, 1143-1151
Algebra i Analiz 4 (1992), No.6, 103-113
Zentralblatt: 0848.17036
Description: Including central extensions.
Availability: hardcopy
Science and totalitarism: the 70s
Zvezda, 1998, N8 (in Russian)
Availability: zvezda.ps.gz
Graded Lie algebras and dynamical systems
DOI: 10.1023/A:1019799409716
Acta Appl. Math. 73 (2002), 239-249
arXiv:math.DS/0203018
ESI-1086 (?)
Abstract: The general class of the graded Lie algebras is defined. These algebras could be constructed using an arbitrary dynamical systems with discrete time and with invariant measure. In this papers we consider the case of the central extension of Lie algebras which corresponds to the ordinary crossed product (as associative algebra) - series A. The structure of those Lie algebras is similar to Kac-Moody algebras, and these are a special case of so called algebras with continuous root system which were introduced by author with M.Saveliev in 90-th. The central extension open a new possibilty in algebraic theory of dynamical systems.
Description: Some interesting constructions of Lie algebras which seem to be close to current.
Two lectures on the asymptotic representation theory and statistics of Young diagrams
LNM 1815 (2003), 161-182
Vershik, A. and Dobrynin, S.
Geometrical approach to the free sovable groups
math.GR/0405008
Description: Cayley graph of a finitely generated group G is considered as one-dimensional complex; its homology group with integer coefficients is considered as G-space.
Vershik, A.M. and Gelfand, I.M. and Graev, M.I.
Representations of the group SL(2,R), where R is a ring of functions
Rus. M. Surv. 28(1973)
Irreducible representations of the group G^X and cohomology
Funct. Anal. Appl. 8(1974), N2
Description: current groups
Vershik, A.M. and Okounkov A.Yu.
A new approach to the representation theory of the symmetric groups. II
URL: http://www.pdmi.ras.ru/znsl/2004/v307.html http://springerlink.metapress.com/openurl.asp?genre=article&issn=1072-3374&volume=131&issue=2&spage=5471
Zapiski Nauchn. Sem. POMI 307(2004), 57-98
J. Math. Sci. 131(2005), N2, 5471 - 5494
Description: p. 80 - "Young graph", like in my mythical "Young diagrams" spectral sequences.
Vershik, A.M. and Sergeev, A.N.
A new approach to the representation theory of the symmetric groups. IV. $ \Bbb Z_{2}$-graded groups and algebras
arXiv:0801.2496
Description: Theory of semisimple finite-dimensional superalgebras is outlined.
Vershik, A.M. and Shoikhet, B.B.
Graded Lie algebras whose Cartan subalgebras is the algebras of polynomials in one variable
DOI: 10.1007/BF02551403
Theor. Math. Phys. 123 (2000), N2, 345-352
Vezzosi, Gabriele and Vinogradov, Alexandre M.
On higher order analogues of de Rham cohomology
Differential Geometry and its Applications 19(2003), N1, 29-59
Abstract: Higher order Spencer complexes. Refs. to earlier papers of Vinogradov. Not very lucid.
Availability: science.pdf
Viana, Marlos
On a class of patterned matrices
Description: Some funky (but elementary) oeprations on the set of (covariance?) matrices turning them into algebras or groups. Not clear what for.
Availability: 943b.pdf
Viennot, J.
Algebres de Lie libres et monoides libres
LNM 691(1978)
Description: bases of free Lie alg., not fitting into the Shirshov's scheme
Vignéras, M.-F.
Représentations l-modulaires d'un groupe réductif p-adique avec l ≠ p
Birkhäuser, 1996; hardcover, 233 pp.
Availability: hardcopy (book)
Villarreal, Raphael H.
Monomial algebras
M. Dekker, 2001, 474 pp.
Description: Groebner bases, minimal resolutions, Hilbert Nullstellensatz, associated graded algebras, generators, Koszul homology, ...
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Vinberg, E.B.
Properties of the root decomposition of a semisimple Lie algebra over an algebraically nonclosed field
Funct. Anal. Prilozh. 9 (1975), N1, 2-24
Availability: hardcopy
The Weyl group of a graded Lie algebra
DOI: 10.1070/IM1976v010n03ABEH001711
Math. USSR Izv. 10 (1976), 463-495
Description: Classical simple Lie algebras.
Availability: IZV_10_3_A03.pdf
On certain commutative subalgebras of a universal enveloping algebra
Math. USSR Izv. 36 (1991), N1, 1-
Description: Commutative subalgebras under Poisson bracket in S(L) are lifted to U(L).
Availability: hardcopy
Generalized derivations of algebras
Third Siberian school on algebra and analysis (ed. L.A. Bokut' et al.), AMS Transl. 163 (1995), 185-188
Zentralblatt: 0828.16040
Availability: p185.png (first page only)
Construction of the exceptional simple Lie algebras
Lie Groups and Invariant Theory (ed. E. Vinberg), AMS, 2005
google books
Vinberg, E.B. and Onishchik, A.L.
Seminar on Lie groups and algebraic groups
2nd ed., URSS, 1995 (in Russian); paperback, 343 pp.
Springer, 1990
Zentralblatt: 0648.22009 0722.22004
Availability: hardcopy (book); absent on amazon; Kolkhoz (Russian edition)
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Vinogradov, A.M. and Krasilshchik, I.S. and Lychagin, V.V.
Vvedenie v geometriyu nelineinykh differencialnykh uravnenii
Nauka, 1986 (in Russian); hardcover, 334 pp.
Availability: hardcopy (book); Euler's library
Vinogradov, A.M.
Cohomological Analysis of Partial Differential Equations and Secondary Calculus
AMS, 2001, 247 pp.
Availability: 2001-cohomological.djvu
Vinogradov, I.M.
Elements of Number Theory
Dover, 1954 (translation from the 5th Russian edition, 1949); paperback, 227 pp.
Availability: hardcopy (book); Kolkhoz' obmennik
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Vitale, Enrico M.
On the categorical structure of H^2
Journal of Pure and Applied Algebra Volume 177, Issue 3, 1 February 2003, Pages 303-308
Abstract: The categorical structure of H^2 is shown to be a particular instance of the cokernel of a morphism between symmetric categorical groups.
Viviani, Filippo
Restricted simple Lie algebras and their infinitesimal deformations
Proc. Conf. "From Lie Algebras to Quantum Groups", Centro Internacional de Matematica no. 28, 2006
arXiv:math.RA/0702755
Description: Exposition of results of other papers?
Infinitesimal deformations of restricted simple Lie algebras. I
arXiv:math.RA/0612861
J. Algebra, to appear
Description: H^2(L,L). Claimed to be re-proof of Dzhumadildaev's results.
Deformations of restricted simple Lie algebras II
arXiv:math.RA/0702499
Description: Infinitesimal deformations of contact and Hamiltonian.
Deformations of the restricted Melikian Lie algebra
arXiv:math.RA/0702594
Comm. Alg., to appear
Description: Infinitesimal deformations.
Deformations of simple finite group schemes
arXiv:0705.0821
Description: Low-dimensional ordinary and restricted cohomology of modular Lie algebras.
Vizman, Cornelia
Central extensions of the Lie algebra of symplectic vector fields
J. Lie Theory 16 (2006), no. 2, 297--309
Zentralblatt: (me)
Availability: hardcopy
Invariant forms on Lie algebra extensions
DOI: 10.1080/00927870601169226
Comm. Algebra 35 (2007), N5, 1761-1776
Availability: 778211673.pdf
Vladimirov, D.A.
Bulevy algebry
Nauka, 1969 (in Russian)
Availability: Kolkhoz
Vladimirov, S.A.
Gruppy simmetrii differencialnykh uravnenii i relyativistskie polya
Availability: symm-rel.djvu
Vlasov, N.A.
Ob ustoichivykh mnogoobraziyakh algebr Lie
Vestnik MGU 1997, N4, 24-29
Description: Identities of W_1 and sl(2).
Volkov, M.V.
Struktury mnogoobrazii algebr
Mat. Sb. 109(1979), N1, 60-79
Volobuev, I.P. and Kubyshin, Yu.A.
Diiferencialnaya geometriya i algebry Lie i ikh prilozheniya v teorii polya
URSS, 1998 (in Russian); hardcover, big format, 222 pp.
Availability: hardcopy (book)
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Volodin, L.
Algebraic K-theory as an extraordinary homology theory on the category of associative rings with a unit
Izvestiya AN SSSR 35(1971), 844-873
Volpert, Klaus
A spectral sequence connecting the Spencer cohomology of a transitive Lie algebra with its deformation cohomology
Algebras Groups Geom. 7(1990), 313-344
Zentralblatt: 0737.17007
Availability: hardcopy; Spencer_paper.pdf
Finite spectral sequences and Massey powers in the deformation theory of graded Lie algebras and associative algebras
JPAA 87(1993), 281-300
Zentralblatt: 0796.17020
Availability: hardcopy
Volvachev, R.T.
Elementary theory of modules
Vestsi Akad. Nauk BSSR Ser. Fiz.-Mat. Nauk 4 (1967), 7-12
38(1969), p.5 by Yu.L. Ershov
Positive and elementary linear groups
Dokl. Akad. Nauk BSSR 12 (1968), 753-755
MR 39#1316
MR Review: Let $M\subseteq G$, $G$ a group. Let $A$ be the set of all formulas of elementary logic with equality, and with one free variable $x$, which are true in $G$ for each $x\in M$. The closure $\overline M$ of $M$ is the set of all $x\in G$ for which each member of $A$ is true. This defines the elementary topology on $G$. The positive topology is obtained if only positive formulas are considered. The article contains some elementary results concerning connections between these two topologies and the Zariski topology on the group of non-singular matrices over a field.
Linear groups as axiomatizable classes of models
Dokl. Akad. Nauk BSSR 14 (1970), 209-211
MR 43#4653
Zentralblatt: 0243.08005
MR Review: Suppose that $\Gamma$ is a class of groups closed under ultraproducts and subgroups and that $P$ is a class of fields closed under ultraproducts. The author shows that the class consisting of those groups in $\Gamma$ that admit a faithful linear representation of degree $n$ over some field in $P$ forms an elementary class (in the wide sense). The proof depends on H. J. Keisler's characterization of elementary classes [Nederl. Akad. Wetensch. Proc. Ser. A 64 (1961), 477--495; MR 25 #3816].
Availability: hardcopy
Volvachev and Suprunenko
Lineinye gruppy
Algebra. Topologiya. Geometriya. 4, VINITI, 1967, 45-62
Availability: absent in VU, UVA, CWI, Iceland
Voronov, A.A. and Gerstenhaber, M.
Higher operators on the Hochschild complex
Funct. Anal. Appl. 29(1995), No.1, 1-5
Availability: hardcopy
Voronov, Alexander A.
Semi-infinite homological algebra
DOI: 10.1007/BF01244304
Invent. Math. 113 (1993), No.1, 103-146
Zentralblatt: 0805.17015
Semi-infinite cohomology of Lie algebras
Algebraic Groups and Their Generalizations (ed. William J. Haboush and Brian J. Parshall), Part 2, AMS, 1994
Notes on universal algebra
arXiv:math.QA/0111009
Description: A survey: deformations, deformation quantization (Kontsevich), operads, A_\infty algebras.
Voronov, Theodore Th.
On the Poisson envelope of a Lie algebra. "Noncommutative" moment space
Funct. Anal. Appl. 29(1995), No.3, 196-199
Description: For an arbitrary Lie superalgebra L, a Z-graded Poisson algebra E(L) (defined on tensor powers of L) is constructed such U(L) and S(L) are its factor-algebras.
Availability: hardcopy
Voskresenskii, V.E.
Behavior of semisimple algebraic groups when the base field is extended
Doklady (?) circa 1964, 1299-1301
Description: Forms of classical Lie algebras, Galois cohomology.
Availability: hardcopy
Vovsi, Samuel N.
Topics in Varieties of Group Representations
LMS Lect. Notes Ser. 163, Cambridge Univ. Press, 1991; paperback, 200 pp.
Description: Corollary 4.5.4. Every finitely generated PI-algebra over a noetherian Jacobson domain K satisfies all identities of the algebra M_r(K) for some r (over fields this was proved earlier by Lewin).
Availability: hardcopy (book)
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Vu, Le Anh
On a Subclass of 5-Dimensional Solvable Lie Algebras Which Have 3-Dimensional Commutative Derived Ideal
math.RT/0603076
(re)generated at Mon Sep 29 19:49:05 GMT 2008