Related Hom-rhizaform algebras and Rota-Baxter Operators, Hom-Rhizaform Family Algebras

TL;DR

This paper introduces Hom-rhizaform family algebras, a generalization of Hom-rhizaform algebras, demonstrating how Rota-Baxter operators can generate new structures and expanding the theory of Hom-algebras.

Contribution

It defines Hom-rhizaform family algebras and shows how Rota-Baxter operators can be used to construct and classify these new algebraic structures.

Findings

Rota-Baxter operators generate new Hom-rhizaform algebras

Classification of Hom-rhizaform family algebras established

Cocycle cones associated with these algebras identified

Abstract

This paper explores the link between Hom-rhizaform algebras and Rota-Baxter operators. We define a new structure, the Hom-rhizaform family algebra, which is a more general version of the Hom-rhizaform algebra. The main finding is that Rota-Baxter operators can be used to construct new Hom-rhizaform algebras. This work expands the theory of Hom-algebras by showing a new way to apply Rota-Baxter operators. Finally, we establish the classification of these algebras as well as their corresponding cocycle cones.