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About Leibniz cohomology and deformations of Lie algebras

By Alice Fialowski, Louis Magnin and Ashis Mandal

Abstract

We compare the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones by a very elementary approach. The comparison gives some conditions, which are easy to verify for a given Lie algebra, for deciding whether it has more Leibniz deformations than just the Lie ones. We also give the complete description of a Leibniz (and Lie) versal deformation of the 4-dimensional diamond Lie algebra, and study the case of its 5-dimensional analogue.Comment: 17 page

Topics: Mathematics - Quantum Algebra, Mathematics - K-Theory and Homology, 17A32, 17B56, 14D15
Year: 2011
OAI identifier: oai:arXiv.org:1103.2694
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