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.

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References in corpus (6)

• Hom-algebras and homology
• On unitality conditions for Hom-associative algebras
• Hom-alternative algebras and Hom-Jordan algebras
• On Hom type algebras
• Hom-Algebras and Hom-Coalgebras
• On hom-algebras with surjective twisting

Cited by in corpus (1)

• Some characterizations of Hom-Leibniz algebras