Supercommutator algebras of right (Hom-)alternative superalgebras

TL;DR

This paper explores the algebraic structures called Hom-Bol superalgebras, showing how they relate to right (Hom-)alternative superalgebras and their supercommutator algebras, expanding the understanding of these algebraic systems.

Contribution

It introduces Hom-Bol superalgebras, proves their closure under even self-morphisms, and demonstrates how supercommutator algebras of right Hom-alternative superalgebras naturally form Hom-Bol superalgebras.

Findings

Supercommutator algebra of a right alternative superalgebra is a Bol superalgebra.

Hom-Bol superalgebras are closed under even self-morphisms.

Supercommutator algebra of a right Hom-alternative superalgebra has a Hom-Bol superalgebra structure.

Abstract

The supercommutator algebra of a right alternative superalgebra is a Bol superalgebra. Hom-Bol superalgebras are defined and it is shown that they are closed under even self-morphisms. Any Bol superalgebra along with any even self-morphism is twisted into a Hom-Bol superalgebra. The supercommutator algebra of a right Hom-alternative superalgebra has a natural Hom-Bol superalgebra structure.