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Keywords:
Akivis algebra; Hom-associative algebra; Hom-Lie algebra; Hom-Akivis algebra; Hom-Malcev algebra
Akivis algebra; Hom-associative algebra; Hom-Lie algebra; Hom-Akivis algebra; Hom-Malcev algebra
Summary:
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 Hom-Akivis algebras can be obtained from Akivis algebras by twisting along algebra endomorphisms and that the class of Hom-Akivis algebras is closed under self-morphisms. It is pointed out that a Hom-Akivis algebra associated to a Hom-alternative algebra is a Hom-Malcev algebra.
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