Quantum Quasi-Shuffle 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 $(V,m,\sigma )$.

12 pages;title is changed;abstract and introduction are extended;Section 2 is rewritten;accepted for publication in Lett. Math. Phys

References in corpus (3)

• Multiple $q$-Zeta Values
• Mixable Shuffles, Quasi-shuffles and Hopf Algebras
• Quasi-shuffle products

Cited by in corpus (4)

• From quantum quasi-shuffle algebras to braided Rota-Baxter algebras
• Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras
• Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras
• Coherent unit actions on braided operads and Hopf algebras