English

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