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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

Provided by:
arXiv.org e-Print Archive

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