Quantum quasi-shuffle algebras II. Explicit formulas, dualization, and representations
arXiv:1302.5888
Abstract
Using the concept of mixable shuffles, we formulate explicitly the quantum quasi-shuffle product, as well as the subalgebra generated by primitive elements of the quantum quasi-shuffle bialgebra. We construct a braided coalgebra structure which is dual to the quantum quasi-shuffle algebra. We provide representations of quantum quasi-shuffle algebras on commutative braided Rota-Baxter algebras. As an application, we establish a formal power series whose terms come from a special representation of some kind of quasi-shuffle algebra and whose evaluation at 1 is the multiple -zeta values.
23 pages, it is an extension of Section 1-Section 4 of the paper arXiv:1105.4347, representations of quantum quasi-shuffle algebras are constructed. Some typos are corrected