Explicit results concerning quantum quasi-shuffle algebras and their applications

TL;DR

This paper explicitly formulates the quantum quasi-shuffle product using mixable shuffles, describes the subalgebra generated by primitive elements, and explores applications to Rota-Baxter and tridendriform algebras.

Contribution

It provides explicit formulas for quantum quasi-shuffle products and a detailed description of related subalgebras, advancing understanding of their algebraic structure and applications.

Findings

Explicit quantum quasi-shuffle product formula

Description of subalgebra generated by primitive elements

Examples of Rota-Baxter and tridendriform algebras

Abstract

Using the concept of mixable shuffles, we formulate explicitly the quantum quasi-shuffle product. We also provide a desirable description of the subalgebra generated by the set of primitive elements of the quantum quasi-shuffle bialgebra. A braided coalgebra structure which is dual to the quantum quasi-shuffle in some sense is constructed as well. We use quantum quasi-shuffle algebras to provide examples of Rota-Baxter algebras and tridendriform algebras.