Hom-Alternative, Hom-Malcev and Hom-Jordan superalgebras

TL;DR

This paper explores the properties of Hom-alternative, Hom-Malcev, and Hom-Jordan superalgebras, establishing their interrelations and generalizing key identities within these algebraic structures.

Contribution

It proves that Hom-alternative superalgebras are both Hom-Malcev-admissible and Hom-Jordan-admissible, and extends classical identities to the Hom-superalgebra context.

Findings

Hom-alternative superalgebras are Hom-Malcev-admissible

Hom-alternative superalgebras are Hom-Jordan-admissible

Generalizations of identities like the Bruck-Kleinfled function are obtained

Abstract

Hom-alternative, Hom-Malcev and Hom-Jordan superalgebras are $\mathbb{Z}_{2}$-graded generalizations of Hom-alternative, Hom-Malcev and Hom-Jordan algebras, which are Hom-type generalizations of alternative, Malcev and Jordan algebras. In this paper we prove that Hom-alternative superalgebras are Hom-Malcev-admissible and are also Hom-Jordan-admissible. Home-type generalizations of some well known identities in alternative superalgebras, including the $\mathbb{Z}_{2}$-graded Bruck-Kleinfled function are obtained.