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.

19 pages

References in corpus (7)

• Hom-algebras and homology
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• On unitality conditions for Hom-associative algebras
• Hom-alternative algebras and Hom-Jordan algebras
• On Hom type algebras
• Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras
• On hom-algebras with surjective twisting

Cited by in corpus (5)

• Quadratic color Hom-Lie algebras
• One-parameter formal deformations of Hom-Lie-Yamaguti algebras
• Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras
• Color Hom-Akivis algebras, Color Hom-Leibniz algebras and Modules over Color Hom-Leibniz algebras
• Representations, extensions and deformations of $n$-BiHom-Lie algebras