Author： Khmaladze E.
Publisher： Springer Publishing Company
ISSN： 1072-3374
Source： Journal of Mathematical Sciences, Vol.195, Iss.4, 2013-12, pp. : 481-485
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Abstract
In this note, by using a generalized notion of the Leibniz algebra of derivations, we present the constructions of the zero, first, and second non-Abelian Leibniz cohomologies with coefficients in crossed modules, which generalize the classical zero, first, and second Leibniz cohomology. For Lie algebras we compare the non-Abelian Leibniz and Lie cohomologies. We describe the second non-Abelian Leibniz cohomology via extensions of Leibniz algebras by crossed modules.
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