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Enveloping Lie Algebras of Low Dimensional Leibniz Algebras

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DOI: 10.4236/am.2011.28142    4,141 Downloads   7,352 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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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[3] M. K. Kinyon and A. Weinestein, “Leibniz Algebras, Courant Algebroids, and Multiplications on Homogeneous Spaces,” American Journal of Mathematics, Vol. 123, No. 3, 2001, pp. 525-550. doi:10.1353/ajm.2001.0017
[4] S. Albeverio, B. A. Omirov and I. S. Rakhimov, “Varieties of Nilpotent Complex Leibniz Algebras of Dimension Less Than Five,” Communications in Algebra, Vol. 33, No. 5, 2005, pp. 1575-1585. doi:10.1081/AGB-200061038

  
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