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arXiv · 1503.02977

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

Kurusch Ebrahimi-Fard·Dominique Manchon·Johannes Singer
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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.

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Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer. 2016-02-05. The Hopf algebra of (q)multiple polylogarithms with non-positive arguments. https://doi.org/10.1093/imrn%2Frnw128

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