About Leibniz cohomology and deformations of Lie algebras

Details About Leibniz cohomology and deformations of Lie algebras About Leibniz cohomology and deformations of Lie algebras

2011-03-14

arxiv.org/abs/1103.2694v1

Mathematics

Quantum Algebra

17 pages

Scientific paper

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.

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