On a class of Leibniz algebras

Authors

  • Côme Béré

    Université de Ouagadougou
  • Aslao Kobmbaye

    Université de Djamena (Tchad)
  • Amidou Konkobo

    Université de Ouagadougou

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

DOI:

https://doi.org/10.14419/ijams.v3i2.5290

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

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    [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

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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