On a class of Leibniz algebras

Authors and Affiliations

  • Côme Béré Université de Ouagadougou
  • Aslao Kobmbaye Université de Djamena (Tchad)
  • Amidou Konkobo Université de Ouagadougou

About this article

Download PDF

Keywords:

Killing form, Leibniz algebras, Leibniz modules, Representations, Semisimplicity.

Abstract

We pointed out the class of Leibniz algebras such that the Killing form is non degenerate implies algebras are semisimple.

References

[1] S., Ayupov, Sh.A. and Omirov, B.A.,, "Cartan subalgebras, weight spaces and criterion of solvability of finiite dimensional Leibniz algebras.",Rev. Mat. Complut., Vol.19, No.1, (2006), pp.183-195.

[2] D. W. Barnes, "On Engel's theorem for Leibniz algebras", Comm. Algebra, Vol.40, No.1, (2012), 1388-1389, arXiv:1012.0608.

[3] C. J. A. Béré, N . B. Pilabré and A. Kobmbaye "Lie's theorems on soluble Leibniz algebras.", British journal of Mathematics & Computer Science , Vol.4, No.18, (2014), pp.2570-2581.

[4] I. Demir, K. C. Misra and E. Stitzinger "On some structures of Leibniz Algebras, ", arXiv:1307.7672v1 .

[5] J. E. Hymphreys, Introduction to Lie Algebras and Representation Theory, Graduate Texts in Mathematics) Springer (1972).

http://books.google.bf/books?id=SD4DvUFa6QC

[6] G. Masons and G. Yamskulna, "Leibniz Algebras and Lie Algebras", Published online October 23, 2013

http://dxdoi.org/103842/SIGMA2013.063,

[7] R. Schafer, Non associative algebras,

https://www.gutenberg.org/files/25156/25156-pdf.pdf


How to Cite

Béré, C., Kobmbaye, A., & Konkobo, A. (2015). On a class of Leibniz algebras. International Journal of Advanced Mathematical Sciences, 3(2), 147-155. https://doi.org/10.14419/ijams.v3i2.5290