2011/03/14 by Fialowski, Alice, Magnin, Louis, Mandal, Ashis
#14D15 #17A32 #17B56 #FOS: Mathematics #K-Theory and Homology (math.KT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1103.2694
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.