Hom-alternative modules and Hom-Poisson comodules

TL;DR

This paper introduces modules over Hom-alternative algebras and comodules over Hom-Poisson coalgebras, expanding the algebraic framework and providing new constructions, properties, and extension results.

Contribution

It develops the theory of modules over Hom-alternative algebras and comodules over Hom-Poisson coalgebras, including constructions, properties, and morphism extensions.

Findings

Constructed examples of Hom-alternative modules

Proved morphism extension from alternative to Hom-alternative algebras

Established structures of comodules over Hom-Poisson coalgebras

Abstract

In this paper we introduce modules over both left and right Hom-alternative algebras. We give some constructions of left and right Hom-alternative modules and give various properties of both, as well as examples. Then, we prove that morphisms of left alternative algebras extend to morphisms of left Hom-alternative algebras. Next, we introduce comodules over Hom-Poisson coalgebras and show that we may obtain a structure map of a comodule over a Hom-Poisson coalgebra from a given one.