Cohomology and Deformation theory of crossed homomorphisms on Leibniz algebras

Published 18 Nov 2022 in math.RA | (2211.09993v1)

Abstract: In this paper, we construct a differential graded Lie algebra whose Maurer-Cartan elements are given by crossed homomorphisms on Leibniz algebras. This allows us to define cohomology for a crossed homomorphism. Finally, we study linear deformations, formal deformations and extendibility of finite order deformations of a crossed homomorphism in terms of the cohomology theory.

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