From quantum quasi-shuffle algebras to braided Rota-Baxter algebras

TL;DR

This paper introduces braided Rota-Baxter algebras derived from quantum quasi-shuffle algebras, expanding the algebraic framework within braided tensor categories and providing concrete examples via quantum multi-brace algebras.

Contribution

It constructs braided Rota-Baxter algebras from quantum quasi-shuffle algebras and defines the new concept of braided Rota-Baxter algebras in braided tensor categories.

Findings

Construction of Rota-Baxter algebras from quantum quasi-shuffle algebras

Introduction of braided Rota-Baxter algebras in braided tensor categories

Examples using quantum multi-brace algebras in Yetter-Drinfeld modules

Abstract

In this letter, we use quantum quasi-shuffle algebras to construct Rota-Baxter algebras, as well as tridendriform algebras. We also propose the notion of braided Rota-Baxter algebras, which is the relevant object of Rota-Baxter algebras in a braided tensor category. Examples of such new algebras are provided by using quantum multi-brace algebras in a category of Yetter-Drinfeld modules.