Journal of Hebei University(Natural Science Edition) >

2001 , Vol. 21 >Issue 1: 3 - 6

DOI: https://doi.org/10.3969/j.issn.1000-1565.2001.01.002

Criterion for Semisimplicity of an n-Lie Algebra

  • ZHANG Zhi-xue ,
  • LI Hua-jun ,
  • YAN Man-fu
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Online published: 2001-02-25

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Abstract

The authors make a definition of non-degeneracy for the killing form of an n-Lie algebra and prove that an n-Lie algebra is semisimple if and only if its killing form is non-degenerate.The authors also give an example which sho ws that a semisimple n-Lie algebra need not to be a direct sum of simple ideals.

Cite this article

ZHANG Zhi-xue , LI Hua-jun , YAN Man-fu . Criterion for Semisimplicity of an n-Lie Algebra[J]. Journal of Hebei University(Natural Science Edition), 2001 , 21(1) : 3 -6 . DOI: 10.3969/j.issn.1000-1565.2001.01.002

References

[1] FILIPPOV V T. n-Lie algebras [J]. Siberian Mathematical Journal 1985, 26(06).
[2] KASYMOV Sh M. On a theory of n-Lie algebras [J]. Algebra and Logika 1987, 26(03).
[3] Humphreys J E. Introduction to Lie algebras and representation theo ry [M]. New York: Springer-Verlag 1972.
[4] BAI Rui-pu, ZHANG Zhi-xue, LI Hua-jun. The inner deriv atiion algebras of(n+1)-dimensiional n-Lie algebras [J]. Communications in Algebra 2000, 28(06).
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