Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras (original) (raw)

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 sl 2 (K) and describe as formal deformations the q-deformed Witt algebra and Jackson sl 2 (K).

Figures (1)

meaning that the Witt algebra is exactly present in the zero degree term (origin) of the deformation. In the first order term, k = 1, we get

meaning that the Witt algebra is exactly present in the zero degree term (origin) of the deformation. In the first order term, k = 1, we get

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