Deformations of Hom-Alternative and Hom-Malcev algebras

Abstract

The aim of this paper is to extend Gerstenhaber formal deformations of algebras to the case of Hom-Alternative and Hom-Malcev algebras. We construct deformation cohomology groups in low dimensions. Using a composition construction, we give a procedure to provide deformations of alternative algebras (resp. Malcev algebras) into Hom-alternative algebras (resp. Hom-Malcev algebras). Then it is used to supply examples for which we compute some cohomology invariants.

arXiv comment19 pages

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• Constructions and Cohomology of color Hom-Lie algebras
• Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras
• On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras
• Rota-Baxter Hom-Lie-admissible algebras
• Color Hom-Akivis algebras, Color Hom-Leibniz algebras and Modules over Color Hom-Leibniz algebras
• Representations, extensions and deformations of $n$-BiHom-Lie algebras