The Hopf algebra of (q)multiple polylogarithms with non-positive arguments

Abstract

We consider multiple polylogarithms in a single variable at non-positive integers. Defining a connected graded Hopf algebra, we apply Connes' and Kreimer's algebraic Birkhoff decomposition to renormalize multiple polylogarithms at non-positive integer arguments, which satisfy the shuffle relation. The q-analogue of this result is as well presented, and compared to the classical case.

some typos fixed, references updated

References in corpus (7)

• Loday-type Algebras and the Rota-Baxter Relation
• A Lie theoretic approach to renormalization
• Hopf algebras, from basics to applications to renormalization
• Unfolding the double shuffle structure of q-multiple zeta values
• Renormalization of Multiple $q$-Zeta Values
• On Euler's decomposition formula for qMZVs
• Renormalisation of q-regularised multiple zeta values

Cited by in corpus (5)

• Duality and (q-)multiple zeta values
• Renormalisation of q-regularised multiple zeta values
• An algebraic formulation of the locality principle in renormalisation
• Shuffle-type product formulae of desingularized values of multiple zeta-functions
• Relationship between renormalized values of shuffle type and of harmonic type of multiple zeta functions