Color Hom-Akivis algebras, Color Hom-Leibniz algebras and Modules over Color Hom-Leibniz algebras

TL;DR

This paper introduces new algebraic structures called color Hom-Akivis and color Hom-Leibniz algebras, explores their properties, constructions, and relationships, and discusses modules over these algebras.

Contribution

It defines and constructs color Hom-Akivis and Hom-Leibniz algebras, and establishes their connections and module twisting properties.

Findings

Color Hom-Akivis algebras derived from non-associative Hom-algebras

Construction methods for various color Hom-Akivis and Hom-Leibniz algebras

Relationship between Hom-dialgebras and Hom-Leibniz-Poisson algebras

Abstract

In this paper we introduce color Hom-Akivis algebras and prove that the commutator of any color non-associative Hom-algebra structure map leads to a color Hom-akivis algebra. We give various constructions of color Hom-Akivis algebras. Next we study flexible and alternative color Hom-Akivis algebras. Likewise color Hom-Akivis algebras, we introduce non-commutative color Hom-Leibniz-Poisson algebras and presente several constructions. Moreover we give the relationship between Hom-dialgebras and Hom-Leibniz-Poisson algebras; i.e. a Hom-dialgebras give rise to a Hom-Leibniz-Poisson algebra. Finally we show that twisting a color Hom-Leibniz module structure map by a color Hom-Leibniz algebra endomorphism, we get another one.