Hom-alternative modules and Hom–Poisson comodules

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.

Hom-Jordan and Hom-alternative bimodules

“…Remark 2.12. The module Hom-associator given above is a generalization of the one given in [2]. Now, let consider the following notion for Hom-associative algebras.…”

“…First, we start by the following notion, due to [2], where it is called a module over a left (resp. right) Hom-alternative algebra.…”

“…Modules over an ordinary algebra has been extended to the ones of Homalgebras in many works [2,18,21,22].…”

“…give the Hom-module (V, α V ) the structure of a Hom-Jordan A + -bimodule that we denote by V (2) . Corollary 4.16.…”