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

Mathematics

Journal of Generalized Lie Theory and Applications

Author(s): Abdenacer Makhlou, Sergei Silvestrov

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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 sl2 and describe as formal deformations the q-deformed Witt algebra and Jackson sl2.

This article was published in Forum Math 22: 715-739 and referenced in Journal of Generalized Lie Theory and Applications

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