The full cohomology, abelian extensions and formal deformations of Hom-pre-Lie algebras

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 exploits 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.

Keywords

• hom-pre-lie algebra
• cohomology
• abelian extension
• formal deformation