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The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras (2111.11015v1)
Published 22 Nov 2021 in math-ph and math.MP
Abstract: The main purpose of this paper is to provide a full cohomology of a Hom-pre-Lie algebra with coefficients in a given representation. This new type of cohomology exploit strongly the Hom-type structure and fits perfectly with simultaneous deformations of the multiplication and the homomorphism defining a Hom-pre-Lie algebra. Moreover, we show that its second cohomology group classifies abelian extensions of a Hom-pre-Lie algebra by a representation.