The Algebra of a q-Analogue of Multiple Harmonic Series

TL;DR

This paper develops an algebraic framework for a q-analogue of multiple harmonic series, establishing multiplication rules, double shuffle relations, and exploring the structure of linear relations among these q-series.

Contribution

It introduces a new algebraic structure for q-analogues of multiple zeta values, including formulations of double shuffle relations and identities.

Findings

Formulated double shuffle relations for the q-series

Derived a q-analogue of Hoffman's identity

Analyzed the dimension of the space of linear relations

Abstract

We introduce an algebra which describes the multiplication structure of a family of q-series containing a q-analogue of multiple zeta values. The double shuffle relations are formulated in our framework. They contain a q-analogue of Hoffman's identity for multiple zeta values. We also discuss the dimension of the space spanned by the linear relations realized in our algebra.