Rota-Baxter systems on Hom-associative algebras and covariant Hom-bialgebras

TL;DR

This paper extends Rota-Baxter systems to Hom-associative algebras, establishing their connections to Hom-dendriform structures, Hom-Yang-Baxter pairs, and covariant Hom-bialgebras, and explores their perturbations.

Contribution

It introduces Rota-Baxter systems on Hom-associative algebras, linking them to new Hom-structures and constructing covariant Hom-bialgebras from Hom-Yang-Baxter pairs.

Findings

Rota-Baxter systems induce Hom-dendriform structures.

Construction of covariant Hom-bialgebras from Hom-Yang-Baxter pairs.

Analysis of perturbations in covariant Hom-bialgebras.

Abstract

Rota-Baxter systems were introduced by Brzezi\'{n}ski as a generalization of Rota-Baxter operators that are related to dendriform structures, associative Yang-Baxter pairs and covariant bialgebras. In this paper, we define Rota-Baxter systems on Hom-associative algebras and show how they induce Hom-dendriform structures and weak pseudotwistors on the underlying Hom-associative algebra. We introduce Hom-Yang-Baxter pairs and a notion of covariant Hom-bialgebra. Given a Hom-Yang-Baxter pair, we construct a twisted Rota-Baxter system and a (quasitriangular) covariant Hom-bialgebra. Finally, we consider perturbations of the coproduct in a covariant Hom-bialgebra.