# Dimitry Leites - Publications

[Books and chapters in books] [Books edited] [Books translated] [Papers] [Encyclopedia entries] [Workouts of SoS]
* if with co-authors; numbered history-wise

1974

[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, Proceedings of XIII All-Union Scientific Students Conference in Mathematics, Novosibirsk State University, 1974, 94-95 (in Russian).

1975

[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

1976

[6*] The structure of Lie supergroups and Fermi-Bose symmetries (with B.M. Zupnik), Multiple processes at high energy, FAN, Tashkent, 1976, 3-50 (in Russian).

1977

[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 odd differential 2-form). The Schouten bracket was rediscovered in terms of superspaces and dubbed "anti-bracket" in seminal works by I.A. Batalin and G.A. Vilkovisky: Gauge algebra and quantization, Phys. Lett. B 102 (1981), 27-31, MR 82j:81047; Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983), 2567-2582, Erratum: 30 (1984), 508, MR 85i:81068a, MR 85i:81068b.

1979

[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, Lie groups and invariant theory. A.L. Onishchik Festschrift (ed. E. Vinberg), AMS Translations Vol. 213, 2005, 223-239, MR 2006c:17011. This approach is applicable to infinite dimensional Lie (super)algebras as well, see [78].

[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

1980

[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: Thirteen papers in algebra, AMS Translations, Vol. 132, 1986, 67-70. MR 82j:17020b

[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].

1981

[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].

1982

[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].

1983

[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), Group-theoretical methods in physics (ed. M. Markov et al.), Vol. 1, Nauka, Moscow, 1983, 269-273 (in Russian); English translation: Harwood Academic Publ., Chur, 1985, Vol. 1-3, 623-629. MR 90g:17019. For corrections abd full details, see [67] and [B4].

[28*] Kac-Moody superalgebras (with B.L. Feigin and V. Serganova), Group-theoretical methods in physics (ed. M. Markov et al.), Vol. 1, Nauka, Moscow, 1983, 274-278 (in Russian); English translation: Harwood Academic Publ., Chur, 1985, Vol. 1-3, 631-637. MR 90f:17038. For full details, see [96], [97], [98] and [B4].

1984

[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

1985

[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

1986

[34*] Embeddings of $$osp(N|2)$$ and the associated nonlinear supersymmetric equations (with M.V. Saveliev and V. Serganova), Group theoretical methods in physics (ed. M.A. Markov, V.I. Manko and V.V. Dodonov), Nauka, Moscow, 1986, 377-394 (in Russian); English translation: [T2], 255-297. MR 89h:17042 MR 89a:58052

1987

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

1989

[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), Functional integration, geometry and strings, Progr. Phys., 13, Birkhäuser, 1989, 421-432. MR 91h:17025

[38*] A new doubly infinite-dimensional superalgebra with central extension (with M. Chaichian and J. Lukierski), Knots, topology and quantum field theories (ed. L. Lusanna), World Scientific, 1989, 645-652. MR 1146959

[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, Computer Algebra in Scientific Computing, CASC 2004 (ed. V.G. Ganzha, E.W. Mayr and E.V. Vorozhtsov), TUM, Munich, 2004, 307-311, arXiv:math/0404247.

1990

[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, Differential geometric methods in theoretical physics (ed. L.-L. Chan and W. Nahm), Plenum Press, 1990, 633-651. MR 93e:17005

1991

[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), General topology and applications (ed. S. Andima et al.), Lect. Notes Pure Appl. Math., 134, Marcel Dekker, 1991, 217-238; correction to appear. MR 93j:58016

[45*] Classical superspaces and related structures (with V. Serganova and G. Vinel), Differential geometric methods in theoretical physics (ed. C. Bartocci, U. Bruzzo and R. Cianci), Lect. Notes Phys. 375 (1991), 286-297. MR 92k:58018

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

1992

[47*] Analogues of the Riemannian structure for classical superspaces (with E. Poletaeva), Proceedings of the International Conference on Algebra (ed. L.A. Bokut, Yu.L. Ershov and A.I. Kostrikin), Contemp. Math. 131 (1992), Part 1, 603-612. MR 93k:58008

[48*] Simple Lie algebras in characteristic $$2$$ recovered from superalgebras and on the notion of simple finite group (with Yu. Kochetkov), Proceedings of the International Conference on Algebra (ed. L.A. Bokut, Yu.L. Ershov and A.I. Kostrikin), Contemp. Math. 131 (1992), Part 2, 59-67. MR 93g:17035

[49*] Defining relations for classical Lie superalgebras. I. Superalgebras with Cartan matrix or Dynkin-type diagram (with V. Serganova), Topological and geometrical methods in field theory (ed. J. Mickelsson and O. Pekonen), World Scientific, 1992, 194-201. MR 94d:17002

1995

[50*] Supergravities and contact type structures on supermanifolds (with E. Poletaeva), Second International Conference on Algebra (ed. L.A. Bokut, A.I. Kostrikin and S.S. Kutateladze), Contemp. Math. 184 (1995), 267-274. MR 96d:58005

1996

[51*] Defining relations associated with principal $$\mathfrak{sl}(2)$$-subalgebras (with P. Grozman), Contemporary Mathematical Physics. F.A. Berezin memorial volume (ed. P. Dobrushin, R. Minlos, M. Shubin and A. Vershik), AMS Translations, Vol. 175, 1996, 57-67; arXiv:math-ph/0510013. MR 97g:17002

1997

[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), Innovation in mathematics. Proceedings of the 2nd international Mathematica symposium (ed. V. Keränen et al.), Computational Mechanics Publications, Southampton, 1997, 185-192.

[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

1999

[56*] From supergravity to ballbearings (with P. Grozman), Supersymmetries and quantum symmetries (ed. J. Wess and E. Ivanov), Lect. Notes Phys. 524 (1999), 58-67. MR 2000j:83090

2000

[57*] Lie superalgebras of supermatrices of complex size. Their generalizations and related integrable systems (with P. Grozman), Complex analysis and related topics (ed. E. Ramírez de Arellano, M. Shapiro, L. Tovar and N. Vasilevski), Birkhäuser, 2000, 73-105; arXiv:math/0202177. MR 2001a:17008

[58*] Defining relations for simple Lie superalgebras. Lie superalgebras without Cartan matrix (with P. Grozman and E. Poletaeva), Supersymmetries and Quantum Symmetries, SQS'99 (ed. E. Ivanov et al.), Dubna, JINR, 2000, 387-396; arXiv:math/0202152.

[59]  The index theorem for homogeneous differential operators on supermanifolds, Supersymmetries and Quantum Symmetries, SQS'99 (ed. E. Ivanov et al.), Dubna, JINR, 2000, 405-408; arXiv:math-ph/0202024.

[60*] Casimir operators for Poisson Lie superalgebras (with A. Sergeev), Supersymmetries and Quantum Symmetries, SQS'99 (ed. E. Ivanov et al.), Dubna, JINR, 2000, 409-411; arXiv:math/0202180. See also [E7].

[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, Memorial volume dedicated to Misha Saveliev and Igor Luzenko (ed. A.N. Sissakian et al.), JINR, Dubna, 2000, 126-131; arXiv:math/0202184.

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

2001

[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, Noncommutative geometry and representation theory in mathematical physics (ed. J. Fuchs, J. Mickelsson, G. Rozenblioum, A. Stolin, A. Westerberg), Contemp. Math. 391 (2005), 111-121, MR 2006i:17010.

[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), Noncommutative structures in mathematics and physics (ed. S. Duplij and J. Wess), Kluwer, 2001, 13-30. MR 2003d:17025. See [E8].

[69*] An unconventional supergravity (with P. Grozman), Noncommutative structures in mathematics and physics (ed. S. Duplij and J. Wess), Kluwer, 2001, 41-47; arXiv:hep-th/0202115. MR 2003a:83101

[70*] The Howe duality and Lie superalgebras (with I. Shchepochkina), Noncommutative structures in mathematics and physics (ed. S. Duplij and J. Wess), Kluwer, 2001, 93-112; arXiv:math/0202181. MR 2003a:17039

[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

2002

[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, Operator methods in ordinary and partial differential equations (ed. S. Albeverio, N. Elander, W.N. Everitt and P. Kurasov), Birkhäuser, 2002, 267-285. MR 2003g:37134

[77]  On unconventional integration on supermanifolds and cross ratio on classical superspaces, Proceedings of the International Workshop "Supersymmetries and Quantum Symmetries" (ed. E. Ivanov, S. Krivonos, J. Lukierski, A. Pashnev), JINR, Dubna, 2002, 251-262; arXiv:math/0202194.

[78*] Invariant operators on supermanifolds and standard models (with P. Grozman and I. Shchepochkina), Multiple facets of quantization and supersymmetry. Michael Marinov memorial volume (ed. M. Olshanetsky and A. Vainstein), World Scientific, 2002, 508-555; arXiv:math/0202193. MR 2004b:17041

2003

[79*] Defining relations for the exceptional Lie superalgebras of vector fields (with P. Grozman and I. Shchepochkina), The orbit method in geometry and physics. In honor of A.A. Kirillov (ed. C. Duval, L. Guieu and V. Ovsienko), Birkhäuser, 2003, 101-146; arXiv:math-ph/0202025. MR 2004h:17026

[80*] The analogs of the Riemann tensor for exceptional structures on supermanifolds (with P. Grozman and I. Shchepochkina), Fundamental mathematics today. In honor of the 10th anniversary of the Independent University of Moscow (ed. S.K. Lando and O.K. Sheinman), IUM, MCCME, 2003, 89-109; Preprint MPIM-Bonn 2003-18; arXiv:math/0509525. MR 2005g:58009

2004

[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

2005

[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), Lie groups and invariant theory, A.L. Onishchik Festschrift (ed. E. Vinberg), AMS Translations, Vol. 213, 2005, 157-172; arXiv:math/0404139. MR 2006b:17032

[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, Globus (Proceedings of the mathematical seminar of the Independent University of Moscow), Vol. 2, MCCME, 2005, 82-102 (in Russian).

2006

[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

2007

[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), Mathematical Physics (ed. M.J. Aslam, H. Faheem, A. Qadir, Riazuddin and H. Saleem), World Scientific, 2007, 31-38; Preprint MPIMiS 156/2006. MR 2008g:81209

[92]  With and without Felix Berezin, Felix Berezin. Life and death of the mastermind of supermathematics (ed. M. Shifman), World Scientific, 2007, 218-228.

2008

[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

2009

[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

2010

[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

2012

[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.

2014

[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.

Preprints

[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.