Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras

Abstract

The aim of this paper is to extend to Hom-algebra structures the theory of formal deformations of algebras which was introduced by Gerstenhaber for associative algebras and extended to Lie algebras by Nijenhuis-Richardson. We deal with Hom-associative and Hom-Lie algebras. We construct the first groups of a deformation cohomology and give several examples of deformations. We provide families of Hom-Lie algebras deforming Lie algebra $s{l}_2$ and describe as formal deformations the q-deformed Witt algebra and Jackson $s{l}_2$.

16 pages

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