Hom-dendriform algebras and Rota-Baxter Hom-algebras

TL;DR

This paper introduces Rota-Baxter Hom-algebras and generalizes dendriform and tridendriform algebras through twisting identities, exploring their interrelations.

Contribution

It presents the first study of Rota-Baxter Hom-algebras and extends dendriform structures via linear map twisting, establishing connections between these categories.

Findings

Defined Rota-Baxter Hom-algebras

Generalized dendriform and tridendriform algebras

Explored relationships between Hom-algebra categories

Abstract

The aim of this paper is to introduce and study Rota-Baxter Hom-algebras. Moreover we introduce a generalization of the dendriform algebras and tridendriform algebras by twisting the identities by mean of a linear map. Then we explore the connections between these categories of Hom-algebras.