On a class of Leibniz algebras

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


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


  • Keywords


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

  • 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


 

View

Download

Article ID: 5290
 
DOI: 10.14419/ijams.v3i2.5290




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.