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The Classification of Filiform Leibniz Superalgebras of Nilindex n+m 被引量：1

The Classification of Filiform Leibniz Superalgebras of Nilindex n+m
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摘要 In this work the classification of filiform Leibniz superalgebras of nilindex n ＋ m, where n and m （m≠0） are dimensions of even and odd parts, respectively, is obtained. In this work the classification of filiform Leibniz superalgebras of nilindex n ＋ m, where n and m （m≠0） are dimensions of even and odd parts, respectively, is obtained.
作者 Sh.A.AYUPOV B.A.OMIROV A.Kh.KHUDOYBERDIYEV
机构地区 Institute of Mathematics and Information Technologies of Academy Sciences of Uzbekistan Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第2期171-190,共20页 数学学报（英文版）
基金 Supported by INTAS Ref.Nr 04-83-3035 DFG 436USB113/10/01 project (Germany)
关键词 Lie superalgebras Leibniz superalgebras NILPOTENCY characteristic sequence Lie superalgebras, Leibniz superalgebras, nilpotency, characteristic sequence
分类号 O153 [理学—基础数学]
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参考文献16

  • 1Loday, J. L.: Une version non commutative des alg~bres de Lie: les alg~bres de Leibniz. Enseign. Math., 39, 269-293 (1993)
  • 2Albeverio, S., Ayupov, Sh. A., Omirov, B. A.: Cartan subalgebras, weight spaces and criterion of solvability of finite dimensional Leibniz algebras. Revista Matematica Complutense, 19(1), 14-25 (2006)
  • 3Albeverio, S., Ayupov, Sh. A., Omirov, B. A.: On nilpotent and simple Leibniz algebras. Comm. in Algebra., 33(1), 159-172 (2005)
  • 4Ayupov, Sh. A., Omirov, B. A.: On some classes of nilpotent Leibniz algebras. Sib. Math. J., 42(1), 18-29 (2001)
  • 5Balavoine, D.: Deformations et rigidite geometrique des algebras de Leibniz. Comm. in Algebra., 24, 1017-1034 (1996)
  • 6Casas, J. M.: Crossed extensions of Leibniz algebras. Comm. in Algebra., 27(12), 6253-6272 (1999)
  • 7Gao, Y.: The second Leibniz homology group for Kac-Moody Lie algebras. Bull. London Math. Soc., 32, 25-33 (2000)
  • 8Loday, J. L., Pirashvili, T.: Leibniz representations of Leibniz algebras. J. Algebra., 181,414-425 (1996)
  • 9Omirov, B. A.: Conjugacy of Cartan subalgebras of complex finite dimensional Leibniz algebras. Journal of Algebra., 299(1), 25-36 (2006)
  • 10Omirov, B. A.: on transformations of complex filiform Leibniz algebras. DAN RUz., 1, 3-6 (2006)

引证文献1

Acta Mathematica Sinica,English Series
2009年 第2期

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