The Hopf algebra of (q)multiple polylogarithms with non-positive arguments
Number Theory
2017-09-08 v3
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.
Keywords
Cite
@article{arxiv.1503.02977,
title = {The Hopf algebra of (q)multiple polylogarithms with non-positive arguments},
author = {Kurusch Ebrahimi-Fard and Dominique Manchon and Johannes Singer},
journal= {arXiv preprint arXiv:1503.02977},
year = {2017}
}
Comments
some typos fixed, references updated