Deformations of Hom-Alternative and Hom-Malcev algebras

TL;DR

This paper extends the theory of algebra deformations to Hom-Alternative and Hom-Malcev algebras, constructing cohomology groups and providing a method to generate deformations from classical algebras, with concrete examples and invariants.

Contribution

It introduces a deformation cohomology framework for Hom-Alternative and Hom-Malcev algebras and offers a composition method to produce new deformations from existing algebras.

Findings

Constructed low-dimensional deformation cohomology groups.

Developed a procedure to deform classical algebras into Hom-algebras.

Computed cohomology invariants for specific examples.

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.