Quantum Quasi-Shuffle Algebras

TL;DR

This paper explores properties of quantum quasi-shuffle algebras, providing conditions for their construction, their universal property, and applications in basis construction for Yang-Baxter algebras.

Contribution

It introduces new theoretical results on quantum quasi-shuffle algebras, including construction criteria and basis development for specific algebraic structures.

Findings

Established necessary and sufficient conditions for quantum quasi-shuffle product

Proved the universal property of quantum quasi-shuffle algebras

Constructed a linear basis for certain Yang-Baxter algebras

Abstract

We establish some properties of quantum quasi-shuffle algebras. They include the necessary and sufficient condition for the construction of the quantum quasi-shuffle product, the universal property, and the commutativity condition. As an application, we use the quantum quasi-shuffle product to construct a linear basis of $T(V)$, for a special kind of Yang-Baxter algebras $(V,m,\sigma)$.