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About Leibniz cohomology and deformations of Lie algebras

2011

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.

Leibniz algebraPure mathematicsAlgebra and Number TheoryMathematics::Rings and AlgebrasInfinitesimal deformationK-Theory and Homology (math.KT)17A32 17B56 14D15CohomologyMathematics::K-Theory and HomologyLie algebraMathematics - Quantum AlgebraMathematics - K-Theory and HomologyFOS: MathematicsQuantum Algebra (math.QA)Mathematics
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