Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras

TL;DR

This paper introduces Hom-Maltsev, Hom-alternative, and Hom-Jordan algebras, establishing their relationships and generalizing key identities in alternative algebras within the Hom-framework.

Contribution

It defines Hom-Maltsev and Hom-Jordan algebras and proves that Hom-alternative algebras are admissible for both, also deriving generalized identities like Moufang identities.

Findings

Hom-alternative algebras are Hom-Maltsev-admissible

Hom-alternative algebras are Hom-Jordan-admissible

Hom-type identities generalize classical alternative algebra identities

Abstract

Hom-Maltsev(-admissible) algebras are defined, and it is shown that Hom-alternative algebras are Hom-Maltsev-admissible. With a new definition of a Hom-Jordan algebra, it is shown that Hom-alternative algebras are Hom-Jordan-admissible. Hom-type generalizations of some well-known identities in alternative algebras, including the Moufang identities, are obtained.