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Special odd Lie superalgebras in prime characteristic

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Abstract

Let g be a finite dimensional special odd Lie superalgebra over an algebraically closed field \(\mathbb{F}\) of characteristic p > 3. The sufficient and necessary condition is given for g possessing a nondegenerate associative form and in this case the second cohomology group H2(g, \(H^2 (\mathfrak{g},\mathbb{F})\)) is completely determined.

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References

  1. Bai W, Liu W D, Ni L. Derivations of the finite dimensional special odd Hamiltonian superalgebra and its derived subalgebras. ArXiv: 1007.1098

  2. Chiu S. Central extensions and H 1(L, L*) of the graded Lie algebras of Cartan type. J Algebra, 1992, 149: 46–67

    Article  MathSciNet  MATH  Google Scholar 

  3. Farnsteiner R. Central extensions and invariant forms of graded Lie algebras. Algebra Groups Geom, 1986, 3: 431–455

    MathSciNet  MATH  Google Scholar 

  4. Farnsteiner R. Dual space derivations and H 2(L, \(\mathbb{F}\)) of graded Lie algebras. Canad J Math, 1987, 39: 1078–1106

    Article  MathSciNet  MATH  Google Scholar 

  5. Farnsteiner R. The associative forms of Cartan type Lie algebras. Trans Amer Math Soc, 1986, 295: 417–427

    Article  MathSciNet  MATH  Google Scholar 

  6. Fu J Y, Zhang Q C, Jiang C P. The Cartan-type modular Lie superalgebra KO. Commun Algebra, 2006, 34: 107–128

    Article  MathSciNet  MATH  Google Scholar 

  7. Kac V G. Lie superalgebras. Adv Math, 1977, 26: 8–96

    Article  MATH  Google Scholar 

  8. Kac V G. Classification of infinite dimensional simple linearly compact Lie superalgebras. Adv Math, 1998, 139: 1–55

    Article  MathSciNet  MATH  Google Scholar 

  9. Liu WD, He Y H. Finite-dimensional special odd Hamiltonian superalgebras in prime characteristic. Commun Contemp Math, 2009, 11: 523–546

    Article  MathSciNet  MATH  Google Scholar 

  10. Liu W D, Yuan J X. Finite dimensional special odd contact superalgebras over a field of prime characteristic. ArXiv: 0911.3466

  11. Liu W D, Zhang Y Z, Wang X L. The derivation algebra of the Cartan-type Lie superalgebra HO. J Algebra, 2004, 273: 176–205

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang Y, Zhang Y Z. The associative forms of graded Cartan type Lie superalgebras. Chin Adv Math, 2000, 29: 65–70

    MATH  Google Scholar 

  13. Wang Y, Zhang Y Z. Derivation algebra der(H) and central extensions of Lie superalgebras. Commun Algebra, 2004, 32: 4117–4131

    Article  MATH  Google Scholar 

  14. Xie W J, Zhang Y Z. Second cohomology of the modular Lie superalgebra of Cartan type K. Algebra Colloq, 2009, 16: 309–324

    MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology, Harbin, 150006, China

    WenDe Liu & JiXia Yuan

  2. School of Mathematical Sciences, Harbin Normal University, Harbin, 150025, China

    WenDe Liu

Authors
  1. WenDe Liu
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  2. JiXia Yuan
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Correspondence to JiXia Yuan.

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Liu, W., Yuan, J. Special odd Lie superalgebras in prime characteristic. Sci. China Math. 55, 567–576 (2012). https://doi.org/10.1007/s11425-011-4316-4

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  • DOI: https://doi.org/10.1007/s11425-011-4316-4

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