Hom-Akivis 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.