Skip to main content
Log in

A class of generalized odd Hamiltonian Lie superalgebras

  • Research Article
  • Published:
Frontiers of Mathematics in China Aims and scope Submit manuscript

Abstract

We study class of finite-dimensional Cantan-type Lie superalgebras HO(m) over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO(m).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Celousov M J. Derivations of Lie algebras of Cartan-type. Izv Vyssh Uchebn Zaved Mat, 1970, 98(7): 126–134 (in Russian)

    MathSciNet  Google Scholar 

  2. Farnsteiner R. Derivations and central extensions of finitely generated graded Lie algebras. J Algebra, 1988, 118(1): 33–45

    Article  MATH  MathSciNet  Google Scholar 

  3. Fu J Y, Zhang Q C, Jiang C P. The Cartan-type modular Lie superalgebra KO. Comm Algebra, 2006, 34(1): 107–128

    Article  MATH  MathSciNet  Google Scholar 

  4. Grabowski J, Poncin N. Derivations of the Lie algebras of differential operators. Indag Math (NS), 2005, 16(2): 181–200

    Article  MATH  MathSciNet  Google Scholar 

  5. Kac V G. Lie superalgebras. Adv Math, 1977, 26(1): 8–96

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Liu W D, Zhang Y Z, Wang X L. The derivation algebra of the Cartan-type Lie superalgebra HO. J Algebra, 2004, 273(1): 176–205

    Article  MATH  MathSciNet  Google Scholar 

  8. Liu W D, Zhang Y Z. Finite-dimensional odd Hamiltonian superalgebras over a field of prime characteristic. J Aust Math Soc, 2005, 79(1): 113–130

    Article  MATH  MathSciNet  Google Scholar 

  9. Liu W D, Zhang Y Z. Automorphism groups of restricted Cartan-type Lie superalgebras. Comm Algebra, 2006, 34(10): 3767–3784

    Article  MATH  MathSciNet  Google Scholar 

  10. Ma L L, Chen L Y, Zhang Y Z. Finite-dimensional simple modular Lie superalgebra M. Front Math China, 2013, 8(2): 411–441

    Article  MATH  MathSciNet  Google Scholar 

  11. Petrogradski V M. Identities in the enveloping algebras for modular Lie superalgebras. J Algebra, 1992, 145(1): 1–21

    Article  MathSciNet  Google Scholar 

  12. Scheunert M. The Theory of Lie Superalgebras. Lecture Notes in Math, Vol 716. Berlin-Heidelberg-New York: Springer-Verlag, 1979

    MATH  Google Scholar 

  13. Shen G Y. New simple Lie algebras of characteristic p. Chinese Ann Math Ser B, 1983, 4(3): 329–346

    MathSciNet  Google Scholar 

  14. Strade H, Farnsteiner R. Modular Lie algebras and their representations. Monographs and Textbooks in Pure and Applied Math, 116. New York: Marecl Dekker, Inc, 1988

    MATH  Google Scholar 

  15. Su Y C. Classification of finite-dimensional modules of the Lie superalgebras rmsl(2/1). Comm Algebra, 1992, 20(11): 3259–3278

    Article  MATH  MathSciNet  Google Scholar 

  16. Wang Y, Zhang Y Z. Derivation algebra Der(H) and central extensions of Lie superalgebras. Comm Algebra, 2004, 32(10): 4117–4131

    Article  MATH  MathSciNet  Google Scholar 

  17. Xu X N, Zhang Y Z, Chen L Y. The finite-dimensional modular Lie superalgebra γ. Algebra Colloq, 2010, 17(3): 525–540

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang Q C, Zhang Y Z. Derivation algebras of modular Lie superalgebras W and S of Cartan-type. Acta Math Sci, 2000, 20(1): 137–144

    MATH  MathSciNet  Google Scholar 

  19. Zhang Y Z. Finite-dimensional Lie superalgebras of Cartan-type over field of prime characteristic. Chinese Sci Bull, 1997, 42(9): 720–724

    Article  MATH  MathSciNet  Google Scholar 

  20. Zhang Y Z, Fu H C. Finite-dimensional Hamiltonian Lie superalgebra. Comm Algebra, 2002, 30(6): 2651–2673

    Article  MATH  MathSciNet  Google Scholar 

  21. Zhang Y Z, Liu W D. Modular Lie Superalgebras. Beijing: Science Press, 2004 (in Chinese)

    Google Scholar 

  22. Zhang Y Z, Zhang Q C. The finite-dimensional modular Lie superalgebra Ω. J Algebra, 2009, 321(12): 3601–3619

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qiang Mu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, L., Mu, Q. & Zhang, Y. A class of generalized odd Hamiltonian Lie superalgebras. Front. Math. China 9, 1105–1129 (2014). https://doi.org/10.1007/s11464-014-0415-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11464-014-0415-1

Keywords

MSC

Navigation