Construction of Rota-Baxter algebras via Hopf module algebras

TL;DR

This paper introduces Hopf module algebras and demonstrates how they naturally give rise to Rota-Baxter operators, with applications to quantum groups and their algebraic structures.

Contribution

It defines Hopf module algebras and constructs Rota-Baxter operators from coinvariants, extending the algebraic framework for quantum groups.

Findings

Projection onto coinvariants is an idempotent Rota-Baxter operator of weight -1

Yetter-Drinfeld module algebras can be used to construct Hopf module algebras

Positive parts of quantum groups admit Rota-Baxter algebra structures

Abstract

We propose the notion of Hopf module algebras and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight -1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application, we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures.