Hom-Akivis algebras

TL;DR

This paper introduces Hom-Akivis algebras, explores their construction from non-Hom-associative algebras via twisting, and links them to Hom-Malcev algebras, expanding algebraic structures in Hom-algebra theory.

Contribution

It defines Hom-Akivis algebras and establishes their relation to other Hom-algebra structures, providing a new framework for algebraic twisting methods.

Findings

Hom-Akivis algebras are introduced as a new algebraic structure.

Non-Hom-associative algebras can be obtained by twisting nonassociative algebras.

Hom-Akivis algebras relate to Hom-Malcev algebras through Hom-alternative algebras.

Abstract

Hom-Akivis algebras are introduced. The commutator-Hom-associator algebra of a non-Hom-associative algebra (i.e. a Hom-nonassociative algebra) is a Hom-Akivis algebra. It is shown that non-Hom-associative algebras can be obtained from nonassociative algebras by twisting along algebra automorphisms while Hom-Akivis algebras can be obtained from Akivis algebras by twisting along algebra endomorphisms. It is pointed out that a Hom-Akivis algebra associated to a Hom-alternative algebra is a Hom-Malcev algebra.