Post-Lie algebras related to multiple (q-)zeta values

Abstract: Multiple zeta values became of more interest over the last 25 years due to their appearance in various fields of mathematics and also physics. First, we will describe their algebraic structure in terms of Hoffman’s quasi-shuffle algebras, which are certain deformations of the usual shuffle product. Following Racinet this allows to relate a post-Lie algebra to the multiple zeta values, the double shuffle Lie algebra equipped with the Ihara bracket, which gives a new insight into the algebraic structure of multiple zeta values. We are interested in an analog approach for multiple q-zeta values, which are certain q-series degenerating to multiple zeta values for the limit q to 1. In particular, we will explain some results towards a post-Lie algebra related to multiple q-zeta values.

machine learningcommutative algebraalgebraic geometryalgebraic topologycombinatoricscategory theoryoperator algebrasrings and algebrasrepresentation theory

Audience: researchers in the topic

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Algebraic and Combinatorial Perspectives in the Mathematical Sciences

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