{sigma, tau}-Rota-Baxter operators, infinitesimal Hom-bialgebras and the associative (Bi)Hom-Yang-Baxter equation

TL;DR

This paper introduces {sigma, tau}-Rota-Baxter operators as a twisted variant of classical Rota-Baxter operators, linking them to solutions of the associative (Bi)Hom-Yang-Baxter equation and constructing Hom-pre-Lie algebras from infinitesimal Hom-bialgebras.

Contribution

It defines {sigma, tau}-Rota-Baxter operators and establishes their connection to the associative (Bi)Hom-Yang-Baxter equation and Hom-pre-Lie algebras, expanding the theory of Hom-type algebraic structures.

Findings

Defined {sigma, tau}-Rota-Baxter operators as a twisted generalization.

Connected solutions of the associative (Bi)Hom-Yang-Baxter equation to {sigma, tau}-Rota-Baxter operators.

Constructed Hom-pre-Lie algebras from infinitesimal Hom-bialgebras.

Abstract

We introduce the concept of {sigma, tau}-Rota-Baxter operator, as a twisted version of a Rota-Baxter operator of weight zero. We show how to obtain a certain {sigma, tau}-Rota-Baxter operator from a solution of the associative (Bi)Hom-Yang-Baxter equation, and, in a compatible way, a Hom-pre-Lie algebra from an infinitesimal Hom-bialgebra.