Enveloping Lie Algebras of Low Dimensional Leibniz Algebras

Massoud Amini; Isamiddin Rakhimov; Seyed Jalal Langari

doi:10.4236/am.2011.28142

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Applied Mathematics > Vol.2 No.8, August 2011

Enveloping Lie Algebras of Low Dimensional Leibniz Algebras ()

Massoud Amini, Isamiddin Rakhimov, Seyed Jalal Langari

DOI: 10.4236/am.2011.28142 PDF HTML 4,378 Downloads 7,666 Views Citations

Abstract

We calculate the enveloping Lie algebras of Leibniz algebras of dimensions two and three. We show how these Lie algebras could be used to distinguish non-isomorphic (nilpotent) Leibniz algebras of low dimension in some cases. These results could be used to associate geometric objects (loop spaces) to low dimensional Leibniz algebras.

Keywords

Leibniz Algebra, Enveloping Lie Algebra, Nilpotent Algebra

Share and Cite:

M. Amini, I. Rakhimov and S. Langari, "Enveloping Lie Algebras of Low Dimensional Leibniz Algebras," Applied Mathematics, Vol. 2 No. 8, 2011, pp. 1027-1030. doi: 10.4236/am.2011.28142.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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