[Books and chapters in books] [Books edited] [Books translated] [

* if with co-authors; numbered history-wise

[1] Spectra of graded-commutative rings, Uspekhi Mat. Nauk 29 (1974), no.3, 209-210 (in Russian). MR 399115

[2] Lie supergroups and Lie superalgebras,

[3] A certain analog of the determinant, Uspekhi Mat. Nauk 30 (1975), no.3, 156 (in Russian). MR 396609. Here not only multiplicativity of the Berezinian is announced, but Berezinian is interpreted as a part of the value of the \(K_1\)-functor considered from "super" position. This super \(K_1\)-functor is completely described.

[4*] Supermanifolds (with F. Berezin), Doklady Akad. Nauk SSSR 224 (1975), no.3, 505-508 (in Russian); English translation: Soviet Math. Doklady 16 (1975), no.5, 1218-1222. MR 402795. Paper [1] is rewritten with smooth functions replacing polynomials (hence with "real life" like integration and differential equations enriching the scenery). The word "supermanifold" is introduced.

[5] Cohomology of Lie superalgebras, Funkts. Anal. Prilozh. 9 (1975), no.4, 75-76 (in Russian). English translation: Funct. Anal. Appl. 9 (1975), no.4, 75-76. MR 422372

[6*] The structure of Lie supergroups and Fermi-Bose symmetries (with B.M. Zupnik),

[7*] Integral forms and the Stokes formula on supermanifolds (with J.N. Bernstein), Funkts. Anal. Prilozh. 11 (1977), no.1, 55-56 (in Russian); English translation: Funct. Anal. Appl. 11 (1977), no.1, 55-56. MR 647158. See [B3].

[8*] How to integrate differential forms on supermanifolds (with J.N. Bernstein). Funkts. Anal. Prilozh. 11 (1977), no.3, 70-71 (in Russian); English translation: Funct. Anal. Appl. 11 (1977), no.3, 219-221. MR 455008. See [B3].

[9] New Lie superalgebras, and mechanics, Doklady Akad. Nauk SSSR 236 (1977), no.4, 804-807 (in Russian); English translation: Soviet Math. Doklady 18 (1977), no.5, 1277-1280. MR 650249. The quotient of the Lie superalgebra with the Schouten bracket modulo center is interpreted as an analog of Lie algebra of Hamiltonian vector fields (preserving a non-degenerate and closed

[10*] Irreducible representations of finite dimensional Lie superalgebras of type \(W\) (with J.N. Bernstein), Problems in group theory and homological algebra 2 (1979), 187-193 (in Russian). English translation: Selecta Math. Soviet. 3 (1983/84), 63-68. MR 85i:17021. For a very interesting approach to the description of irreducible representations of finite dimensional vectorial and other "lopsided" Lie (super)algebras, see: V. Serganova, On representations of Cartan type Lie superalgebras,

[11*] Irreducible representations of finite-dimensional Lie superalgebras of series \(W\) and \(S\) (with J.N. Bernstein), Comptes Rendus Acad. Bulgare Sci. 32 (1979), 277-278. MR 80j:17002

[12*] A formula for the characters of irreducible finite-dimensional representations of Lie superalgebras of series \(Gl\) and \(sl\) (with J.N. Bernstein), Comptes Rendus Acad. Bulgare Sci. 33 (1980), no.8, 1049-1051 (in Russian). MR 82j:17020a. For the latest developments, see: J. Brundan, Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra \(\mathfrak{gl}(m|n)\), J. Amer. Math. Soc. 16 (2003), 185-231, arXiv:math/0203011, MR 2003k:17007.

[13] A formula for the characters of irreducible finite-dimensional representations of Lie superalgebras of series \(C\), Comptes Rendus Bulgare Acad. Sci. 33 (1980), no.8, 1053-1055 (in Russian); English translation:

[14] Formulas for the characters of irreducible finite-dimensional representations of simple superalgebras, Funkts. Anal. Prilozh. 14 (1980), no.2, 35-38 (in Russian); English translation: Funct. Anal. Appl. 14 (1980), no.2, 106-109. MR 82d:17004.

[15] Introduction to the theory of supermanifolds, Uspekhi Mat. Nauk 35 (1980), no.1, 3-57 (in Russian); English translation: Russ. Math. Surv. 35 (1980), no.1, 1-64. MR 81j:58003. For more details, see [B3].

[16*] Superalgebra \(B(0,1)\) and explicit integration of the supersymmetric Liouville equation (with A.N. Leznov and M.V. Saveliev), Pisma v ZhETF 32 (1980), no.1, 85-88 (in Russian); English translation: JETP Letters 2 (1980), no.1, 79-81; also published in: Phys. Lett. B 96 (1980), 97-99. MR 82c: 81149

[17*] Examples of simple infinite-dimensional Lie superalgebras of vector fields (with D. Alekseevskii and I. Shchepochkina), Comptes Rendus Acad. Bulgare Sci. 34 (1980), no.9, 1187-1190 (in Russian). MR 82k:17010. For the classification, see [104].

[18*] Felix Alexandrovitch Berezin (Obituary) (with N.N. Bogolyubov, I.M. Gelfand, R.L. Dobrushin, A.A. Kirillov, M.G. Krein, R.A. Minlos, Ya.G. Sinai, M.A. Shubin), Uspekhi Mat. Nauk 36 (1981), no.4, 185-190 (in Russian). English translation: Russ. Math. Surv. 36 (1981), no.4, 209-216. MR 83g:01041

[19*] Invariant differential operators and irreducible representations of Lie superalgebras of vector fields (with J.N. Bernstein), Serdica Bulg. Math. Publ. 7 (1981), 320-334 (in Russian). English translation: Selecta Math. Soviet. 1 (1981), no.2, 143-160. MR 83i:17015a MR 84i:17015. For more details, see [78].

[20] Invariant differential operators and irreducible representations of Lie superalgebras of divergence-free vector fields, Serdica Bulgar. Math. Publ. 8 (1982), 12-15 (in Russian). MR 84h:17014. For more details, see [78].

[21] Irreducible representations of Lie superalgebras of vector fields and invariant differential operators, Funkts. Anal. Prilozh. 16 (1982), no.1, 76-77 (in Russian); English translation: Funct. Anal. Appl. 16 (1982), no.1, 62-64. MR 83j:17011. For more details, see [78].

[22] Representations of Lie superalgebras, Teoret. Mat. Fiz. 52 (1982), no.2, 225-228 (in Russian); English translation: Theor. Math. Phys. 52 (1982), no.2, 764-766. MR 84d:17006. Indecomposable and diagonalizable over the maximal toral subalgebra representations of simple Lie superalgebras are described. For the general case (non-diagonalizable over the torus), see [64].

[23*] The superalgebra \(Q(n)\), the odd trace and the odd determinant (with J.N. Bernstein), Comptes Rendus Acad. Bulgare Sci. 35 (1982), no.3, 285-286. MR 84c:17003. For more details, see [B3].

[24*] The complete integrability of some nonlinear equations of the theory of strings (with A.N. Leznov and M.V. Saveliev), Comptes Rendus Acad. Bulgare Sci. 35 (1982), no.4, 435-438 (in Russian). MR 84f: 58061. For more details, see [T9].

[25*] Integrable systems and Lie superalgebras (with M.A. Semenov-Tian-Shansky), Zapiski Nauchn. Semin. LOMI 123 (1983), 92-97 (in Russian). English translation: J. Soviet Math. 28 (1983), 525-528. MR 84g:58053

[26] Automorphisms and real forms of simple Lie superalgebras of formal vector fields, Problems in group theory and homological algebra 3 (1983), 126-128 (in Russian). MR 87b:17014. The announcement contains several omissions. For a correct result with full details, see: N. Cantarini and V.G. Kac, Automorphisms and forms of simple infinite dimensional linearly compact Lie superalgebras, Intern. J. Geom. Meth. Modern Phys. 3 (2006), no.5-6, 845-867, arXiv:math/0601292, MR 2007m:17032.

[27*] New Lie superalgebras of string theories (with B.L. Feigin),

[28*] Kac-Moody superalgebras (with B.L. Feigin and V. Serganova),

[29*] Solutions of the classical Yang-Baxter equation for simple superalgebras (with V. Serganova), Teor. Mat. Fiz. 58 (1984), no.1, 26-37 (in Russian); English translation: Theor. Math. Phys. 58 (1984), no.1, 16-24. MR 85m:82020. See also erratum and addendum in SoS preprint 31/1988. For more corrections, see: G. Karaali, Constructing \(r\)-matrices on simple Lie superalgebras, J. Algebra 282 (2004), 83-102, arXiv:math/0303246, MR 2005h:17017.

[30] Clifford algebra as superalgebras and quantization, Teor. Mat. Fiz. 58 (1984), no.2, 229-232 (in Russian); English translation: Theor. Math. Phys. 58 (1984), no.2, 150-152. MR 85k:81083.

[31] Lie superalgebras, Itogi Nauki i Tekhniki. Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Vol. 25, 1984, VINITI, Moscow, 3-49 (in Russian). English translation: J. Soviet Math. 30 (1985), no.6, 2481-2512. MR 86f:17019

[32*] Cohomology of Lie superalgebras (with D. Fuchs), Comptes Rendus Acad. Bulgare Sci. 37 (1985), no.12, 1595-1596. MR 87e:17022

[33*] Instantons with gauge supergroup (with R.Yu. Kirillova), Problemy Yadernoi Fiziki i Kosmicheskikh Luchei 24 (1985), no.24 (D.V. Volkov Festschrift), Kharkov Univ. Press, 34-40 (in Russian). MR 88h:53032

[34*] Embeddings of \(osp(N|2)\) and the associated nonlinear supersymmetric equations (with M.V. Saveliev and V. Serganova),

[35] Selected problems of supermanifold theory, Duke Math. J. 54 (1987), no.2, 649-656. MR 89c:58014

[36*] New \(N=6\) infinite-dimensional superalgebra with central extension (with M. Chaichian and J. Lukierski), Phys. Lett. B. 225 (1989), no.4, 347-351. MR 90h:17025

[37*] \(N=6\) from central extension of doubly infinite superalgebras (with M. Chaichian and J. Lukierski),

[38*] A new doubly infinite-dimensional superalgebra with central extension (with M. Chaichian and J. Lukierski),

[39*] Cohomology to compute (with G. Post), Computers and Mathematics (ed. E. Kaltofen and S.M. Watt), Springer, 1989, 73-81. MR 90j: 17033. For an update, see Leites' (super)questions. For investigation of certain computational aspects in the study of Lie algebra cohomology, see: V.V. Kornyak, On the structure of cohomology of Hamiltonian \(p\)-algebras,

[40*] General \(D=1\) local supercoordinate transformations and their supercurrent algebras (with M. Chaichian and J. Lukierski), Phys. Lett. B 236 (1990), no.1, 27-32. MR 91e:81034

[41*] Metasymmetry and Volichenko algebras (with V. Serganova), Phys. Lett. B 252 (1990), no.1, 91-96. MR 92b:17005. See [E8].

[42] Toward classification of classical Lie superalgebras,

[43*] Models of representations of some classical supergroups (with V. Serganova), Math. Scand. 68 (1991), 133-147. MR 92j:17001

[44*] New invariant differential operators on supermanifolds and pseudo-(co)homology (with Yu. Kochetkov and A. Vaintrob),

[45*] Classical superspaces and related structures (with V. Serganova and G. Vinel),

[46*] On the defining relations of quantum superalgebras (with R. Floreanini and L. Vinet), Lett. Math. Phys. 23 (1991), 127-131. MR 92m:17010

[47*] Analogues of the Riemannian structure for classical superspaces (with E. Poletaeva),

[48*] Simple Lie algebras in characteristic \(2\) recovered from superalgebras and on the notion of simple finite group (with Yu. Kochetkov),

[49*] Defining relations for classical Lie superalgebras. I. Superalgebras with Cartan matrix or Dynkin-type diagram (with V. Serganova),

[50*] Supergravities and contact type structures on supermanifolds (with E. Poletaeva),

[51*] Defining relations associated with principal \(\mathfrak{sl}(2)\)-subalgebras (with P. Grozman),

[52*] The highest weight representations of the contact Lie superalgebra on \(1|6\)-dimensional supercircle (with P. Grozman), Czech. J. Phys. 47 (1997), no.11, 1133-1138. MR 99e:17006

[53*] Quivers and Lie superalgebras (with I. Shchepochkina), Czech. J. Phys. 47 (1997), no.12, 1221-1229. MR 99c:16012

[54*] Mathematica-aided study of Lie algebras and their cohomology - from supergravity to ballbearings and magnetic hydrodynamics (with P. Grozman),

[55*] Defining relations for classical Lie algebras of polynomial vector fields (with E. Poletaeva), Math. Scand. 81 (1997), no.1, 5-19; arXiv:math/0510019. MR 98m:17032

[56*] From supergravity to ballbearings (with P. Grozman),

[57*] Lie superalgebras of supermatrices of complex size. Their generalizations and related integrable systems (with P. Grozman),

[58*] Defining relations for simple Lie superalgebras. Lie superalgebras without Cartan matrix (with P. Grozman and E. Poletaeva),

[59] The index theorem for homogeneous differential operators on supermanifolds,

[60*] Casimir operators for Poisson Lie superalgebras (with A. Sergeev),

[61*] Manin-Olshansky triples for Lie superalgebras (with A. Shapovalov), J. Nonlin. Math. Phys. 7 (2000), no.2, 120-125; arXiv:math/0004186. MR 2002f:17051

[62*] Orthogonal polynomials of a discrete variable and Lie algebras of complex-size matrices (with A. Sergeev), Teor. Mat. Fiz. 123 (2000), no.2, Proceedings of M. Saveliev memorial conference, 205--236 (in Russian); English translation: Theor. Math. Phys. 123 (2000), no.2, 582--608; arXiv:math/0509528. MR 2001j:17018

[63*] Realization of Lie algebras and superalgebras in terms of creation and annihilation operators. I (with Č. Burdík, P. Grozman and A. Sergeev), Teor. Mat. Fiz. 124 (2000), no.2, 227-238 (in Russian); English translation: Theor. Math. Phys. 124 (2000), no.2, 1048-1058. MR 2002b:17021. See also: I. Shchepochkina, How to realize a Lie algebra by vector fields, Teor. Mat. Fiz. 147 (2006), no. 3, 450-469 (in Russian); English translation: Theor. Math. Phys. 147 (2006), no.3, 821-838; arXiv:math/0509472, MR 2007e:17019.

[64] Indecomposable representations of Lie superalgebras,

[65] How to superize Liouville equation, J. Nonlin. Math. Phys. 7 (2000), no.3, 263-267; arXiv:hep-th/0007256. MR 2001i:35209

[66*] The Shapovalov determinant for the Poisson superalgebras (with P. Grozman), J. Nonlin. Math. Phys. 8 (2001), no.2, 220-228; arXiv:math/0104287. MR 2002d:17009. See also: M. Gorelik and V. Serganova, Shapovalov forms for Poisson Lie superalgebras,

[67*] Lie superalgebras of string theories (with P. Grozman and I. Shchepochkina), Acta Math. Vietnamica 26 (2001), no.1, 27-63; arXiv:hep-th/9702120. MR 2002c:17034

[68*] Symmetries wider than supersymmetry (with V. Serganova),

[69*] An unconventional supergravity (with P. Grozman),

[70*] The Howe duality and Lie superalgebras (with I. Shchepochkina),

[71*] How to quantize the antibracket (with I. Shchepochkina), Teor. Mat. Fiz. 126 (2001), no.3, 339-369 (in Russian); English translation: Theor. Math. Phys. 126 (2001), no.3, 281-306; arXiv:math-ph/0510048. MR 2002k:17042

[72*] Defining relations for Lie superalgebras with Cartan matrix (with P. Grozman), Czech. J. Phys. 51 (2001), no.1, 1-22; arXiv:hep-th/9702073. MR 2002e:17008

[73*] On Einstein equations on manifolds and supermanifolds (with E. Poletaeva and V. Serganova), J. Nonlin. Math. Phys. 9 (2002), no.4, 394-425; arXiv:math/0306209. MR 2003i:53037

[74*] Defining relations for classical Lie superalgebras without Cartan matrices (with P. Grozman and E. Poletaeva), Homology Homotopy Appl. 4 (2002), 259-275. MR 2003e:17009

[75] The Riemann tensor for nonholonomic manifolds, Homology Homotopy Appl. 4 (2002), 397-407; arXiv:math/0202213. MR 2003g:53138

[76] Supersymmetry of the Sturm-Liouville and Korteveg-de Vries operators,

[77] On unconventional integration on supermanifolds and cross ratio on classical superspaces,

[78*] Invariant operators on supermanifolds and standard models (with P. Grozman and I. Shchepochkina),

[79*] Defining relations for the exceptional Lie superalgebras of vector fields (with P. Grozman and I. Shchepochkina),

[80*] The analogs of the Riemann tensor for exceptional structures on supermanifolds (with P. Grozman and I. Shchepochkina),

[81] On computer-aided solving differential equations and stability study of markets, Zapiski Nauchn. Semin. POMI 312 (2004), 165-187; J. Math. Sci. 133 (2006), no.4, 1464-1476. MR 2006e:34082

[82*] Lie superalgebra structures in \(H^{\cdot}(g;g)\) (with P. Grozman), Czech. J. Phys. 54 (2004), no.11, 1313-1319; arXiv:math/0509469. MR 2005j:17022

[83*] Link invariants and Lie superalgebras (with P. Grozman), J. Nonlin. Math. Phys. 12 (2005), Suppl. 1, 372--379. MR 2005m:17006

[84*] Lie superalgebra structures in \(C^{\cdot}(\mathfrak n; \mathfrak n)\) and \(H^{\cdot}(\mathfrak n; \mathfrak n)\) (with A. Lebedev and I. Shereshevskii),

[85*] Structures of \(G(2)\) type and nonintegrable distributions in characteristic \(p\) (with P. Grozman), Lett. Math. Phys. 74 (2005), no.3, 229-262; arXiv:math/0509400. MR 2006k:17034

[86] Application of Lie algebra cohomology in the national economy,

[87*] Simple Lie superalgebras and nonintegrable distributions in characteristic \(p\) (with S. Bouarroudj), Zapiski Nauch. Semin. POMI 331 (2006), 15-29; J. Math. Sci. 141 (2007), no.4, 1390-1398; arXiv:math/0606682. MR 2007d:17025

[88*] On realizations of the Steenrod algebras (with A. Lebedev and an appendix by P. Deligne), J. Prime Research Math. 2 (2006), 101-112; Preprint MPIMiS 131/2006. MR 2007j:55011

[89] Towards classification of simple finite dimensional modular Lie superalgebras, J. Prime Research Math. 3 (2007), 101-110; arXiv:0710.5638. MR 2009b:17047

[90*] Nonholonomic Riemann and Weyl tensors for flag manifolds (with P. Grozman), Teor. Mat. Fiz. 153 (2007), no.2, 187-219 (in Russian); English translation: Theor. Math. Phys. 153 (2007), no.2, 1511-1538; arXiv:math/0509399. MR 2009m:53128

[91*] On critical dimensions of string theories (with Ch. Sachse),

[92] With and without Felix Berezin,

[93*] New simple modular Lie superalgebras as generalized prolongs (with S. Bouarroudj and P. Grozman), Funkts. Anal. Prilozh. 42 (2008), no.3, 1-9 (in Russian). English translation: Funct. Anal. Appl. 42 (2008), no.3, 161-168; arXiv:0704.0130. MR 2009f:17031. arXiv version contains more details and explanations.

[94*] Shapovalov determinant for loop superalgebras (with A. Lebedev), Teor. Mat. Fiz. 156 (2008), no.3, 378-397 (in Russian); English translation: Theor. Math. Phys. 156 (2008), no.3, 1292-1307. MR 2010i:17035

[95] Tales. In [E3], 302-309 (in Russian).

[96*] Classification of finite dimensional modular Lie superalgebras with indecomposable Cartan matrix (with S. Bouarroudj and P. Grozman), Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5 (2009), 060, 63 pages; arXiv:0710.5149. MR 2010m:17018

[97*] Divided power (co)homology. Presentations of simple finite dimensional modular Lie superalgebras with Cartan matrix (with S. Bouarroudj, P.Grozman and A. Lebedev), Homology Homotopy Appl. 12 (2010), no.1, 237-278; arXiv:0911.0243. MR 2011j:17035

[98*] The classification of almost affine (hyperbolic) Lie superalgebras (with D. Chapovalov, M. Chapovalov and A. Lebedev), J. Nonlin. Math. Phys. 17 (2010), Special issue in memory of F. Berezin, 103-161; arXiv:0906.1860. MR 2012g:17030

[99*] Defining relations for almost affine (hyperbolic) Lie superalgebras (with S. Bouarroudj and P. Grozman), J. Nonlin. Math. Phys. 17 (2010), Special issue in memory of F. Berezin, 163-168; arXiv:1012.0176. MR 2827479

[100*] The Poincaré series of the hyperbolic Coxeter groups with finite volume of fundamental domains (with M. Chapovalov and R. Stekolshchik), J. Nonlin. Math. Phys. 17 (2010), Special issue in memory of F. Berezin, 169-215; arXiv:0906.1596. MR 2012j:20120

[101*] Prolongs of (ortho-)orthogonal Lie (super)algebras in characteristic \(2\) (with U. Iyer and A. Lebedev), J. Nonlin. Math. Phys. 17 (2010), Special issue in memory of F. Berezin, 253-309. MR 2012g:17024. See also [Lebedev].

[102*] Examples of simple vectorial Lie superalgebras in characteristic \(2\) (with U. Iyer, M. Messaoudene and I. Shchepochkina), J. Nonlin. Math. Phys. 17 (2010), Special issue in memory of F. Berezin, 311-374. MR 2012h:17025

[103*] Minkowski superspaces and superstrings as almost real-complex supermanifolds (with S. Bouarroudj, P. Grozman and I. Shchepochkina), Teor. Mat. Fiz. 173 (2012), no.3, 416-440 (in Russian); English translation: Theor. Math. Phys. 173 (2012), no.3, 1687-1708; arXiv:1010.4480.

[104*] Deforms of Lie algebras in characteristic 2: Semi-trivial for Jurman algebras, non-trivial for Kaplansky algebras (with S. Bouarroudj, A. Lebedev and I. Shchepochkina), Math. Res. Lett., to appear; arXiv:1301.2781.

[105*] Classification of simple vectorial Lie superalgebras (with I. Shchepochkina), Preprint MPIM-Bonn 2003-28.

[106*] Infinitesimal deformations of symmetric simple modular Lie algebras and Lie superalgebras (with S. Bouarroudj and P. Grozman), arXiv:0807.3054.

Last modified: Sat Jan 18 07:51:34 BRST 2014