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ANALOGS OF THE ORTHOGONAL, HAMILTONIAN, POISSON, AND CONTACT LIE SUPERALGEBRAS IN CHARACTERISTIC 2

ALEXEI LEBEDEV

Equa Simulation AB, Stockholm, Sweden

https://doi.org/10.1142/S1402925110000854Cited by:18 (Source: Crossref)

Abstract

Over algebraically closed fields of characteristic 2, the analogs of the orthogonal, symplectic, Hamiltonian, Poisson, and contact Lie superalgebras are described. The number of non-isomorphic types, and several properties of these algebras are unexpected, for example, interpretation in terms of exterior differential forms preserved is not applicable to one of these types. The divided powers of differential forms and related (co)homology are introduced.

Keywords:

AMSC: 17B50

References

A. A. Albert, I. Trans. Amer. Math. Soc. 43(3), 386 (1938). Web of Science, Google Scholar
G. Benkart, T. Gregory and A. Premet, AMS Memoir (2008). Google Scholar
F. A. Berezin , The Method of Second Quantization , Pure and Applied Physics 24 ( M. Nauka , 1965 ) . Google Scholar
J. Bernstein and D. Leites, Sel. Math. Sov. 1(2), 143 (1981). Google Scholar
S. Bouarroudj, P. Grozman and D. Leites, Symmetry, Integrability and Geometry: Methods and Applications SIGMA 5(060), 63 (2009), arXiv:0710.5149. Web of Science, Google Scholar
G. Brown, Comm. Algebra 23(3), 941 (1995), DOI: 10.1080/00927879508825259. Crossref, Web of Science, Google Scholar
R. H. Dye, J. Algebra 53(1), 36 (1978), DOI: 10.1016/0021-8693(78)90202-8. Crossref, Web of Science, Google Scholar
P. Grozman, D. Leites and I. Shchepochkina, M. Marinov Memorial Volume, eds. M. Olshanetsky and A. Vainshtein (World Sci., 2002) pp. 508–555, arXiv:math.RT/0202193. Google Scholar
G. G. Ilyuta, Monodromy and vanishing cycles of boundary singularities (Russian), Funktsional. Anal. i Prilozhen 19(3) (1985) 11–21; English translation: Functional Anal. Appl. 19(3) (1985) 173–182; G. G. Ilyuta, Monodromy Groups of Boundary Singularities (Russian), Mat. Sb. 183(5) (1992) 29–42; translation in Russian Acad. Sci. Sb. Math. 76(1) (1993) 23–34 . Google Scholar
S. Konstein, A. Smirnov and I. Tyutin, General form of deformation of Poisson superbracket , arXiv:hep-th/0401023 . Google Scholar
S. E. Konstein and M. A. Vasiliev, J. Math. Phys. 37(6), 2872 (1996), DOI: 10.1063/1.531544. Crossref, Web of Science, Google Scholar
S. E. Konstein, Supersymmetry and quantum field theory (Kharkov, 1997), Lecture Notes in Phys. 509 (Springer, Berlin, 1998) pp. 305–311. Crossref, Google Scholar
S. E. Konstein, An example of simple Lie superalgebra with several invariant bilinear forms , arXiv:math-ph/0112063 . Google Scholar
S. Lando, J. Combinatorial Theory, Series B 80(1), 104 (2000), DOI: 10.1006/jctb.2000.1973. Crossref, Web of Science, Google Scholar
A. Lebedev, D. Leites and I. Shereshevskii, Lie Groups and Invariant Theory, Amer. Math. Soc. Transl. Ser. 2, ed. É. Vinberg (Amer. Math. Soc., Providence, RI, 2005) pp. 157–172, arXiv:math.KT/0404139. Google Scholar
A. Lebedev, Non-degenerate bilinear forms in characteristic 2, related contact forms, simple Lie algebras and superalgebras , arXiv:math.AC/0601536 . Google Scholar
D. Leites, Soviet Math. Doklady 18(5), 1277 (1977). Web of Science, Google Scholar
D. Leites (ed.) (J. Bernstein, S. Bouarroudj, B. Clarke, P. Grozman, A. Lebedev, D. Leites, I. Shchepochkina) Representation Theory. (Vol. 2. Quest for Simple Modular Lie Superalgebras), A. Salam School of Mathematical Sciences, Lahore (2009) . Google Scholar
D. Leites, E. Poletaeva and V. Serganova, J. Nonlinear Math. Physics 9(4), 394 (2002), arXiv:math.DG/0306209 DOI: 10.2991/jnmp.2002.9.4.3. Crossref, Web of Science, Google Scholar
D. Leites and I. Shchepochkina, Teoret. Mat. Fiz. 126(3), 339 (2001), arXiv:math-ph/0510048. Crossref, Web of Science, Google Scholar
D. Leites and I. Shchepochkina, The classification of simple Lie superalgebras of vector fields, preprint MPIM-2003-28 (http://www.mpim-bonn.mpg.de) . Google Scholar
D. Leites, J. Prime Res. Math. 3, 101 (2007), arXiv:0710.5638. Google Scholar
L. Lin, J. East China Norm. Univ. Natur. Sci. 1, 16 (1988). Google Scholar
L. Lin, Comm. Algebra 21(2), 399 (1993), DOI: 10.1080/00927879308824569. Crossref, Web of Science, Google Scholar
Yu. A. Neretin , London Mathematical Society Monographs , New Series, Oxford Science Publications 16 ( The Clarendon Press, Oxford University Press , New York , 1996 ) . Google Scholar
Yu. A. Neretin, Recollections on Felix Alexandrovich Berezin — the Founder of Supermathematics, eds. E. G. Karpelet al. (MCCME, Moscow) p. 382. Google Scholar
A. Premet and H. Strade, Classification of finite dimensional simple Lie algebras in prime characteristics , arXiv:math/0601380 . Google Scholar
Ch. Sachse, Teor. Mat. Fiz. 149(1), 3 (2006). Google Scholar
I. Shchepochkina, Theor. Mat. Fiz. 147(3), 821 (2006), arXiv:math.RT/0509472. Crossref, Web of Science, Google Scholar
R. Steinberg , Lectures on Chevalley Groups ( Yale University , New Haven, Conn. , 1968 ) . Google Scholar