Hom-alternative algebras and Hom-Jordan algebras

TL;DR

This paper introduces Hom-alternative and Hom-Jordan algebras, explores their properties, and provides construction methods from classical algebras, establishing connections between Hom-associative and Hom-Jordan structures.

Contribution

It is the first to define and analyze Hom-alternative and Hom-Jordan algebras, expanding the framework of Hom-algebra theory with new constructions and properties.

Findings

Hom-alternative and Hom-Jordan algebras are well-defined structures.

Construction procedures from classical algebras are established.

Polarization of Hom-associative algebra yields Hom-Jordan algebra.

Abstract

The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a polarization of Hom-associative algebra leads to Hom-Jordan algebra.