Cohomology and Deformations of Hom-algebras

Details Cohomology and Deformations of Hom-algebras Cohomology and Deformations of Hom-algebras

2010-05-04

arxiv.org/abs/1005.0456v1

Mathematics

Rings and Algebras

Scientific paper

The purpose of this paper is to define cohomology structures on Hom-associative algebras and Hom-Lie algebras. The first and second coboundary maps were introduced by Makhlouf and Silvestrov in the study of one-parameter formal deformations theory. Among the relevant formulas for a generalization of Hochschild cohomology for Hom-associative algebras and a Chevalley-Eilenberg cohomology for Hom-Lie algebras, we define Gerstenhaber bracket on the space of multilinear mappings of Hom-associative algebras and Nijenhuis-Richardson bracket on the space of multilinear mappings of Hom-Lie algebras. Also we enhance the deformations theory of this Hom-algebras by studying the obstructions.

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