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The Hopf Algebra of ($q$-)Multiple Polylogarithms with Non-positive Arguments: Table 1

Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer
2016 International mathematics research notices  

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2015 pre-print arXiv:1503.02977v2 fatcat:6zp4f2n7ircvtbfjn43wrjpsha

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2016 accepted
arXiv:1503.02977v3 fatcat:aomna33qejazzmie44tcjdt2ne
2015 pre-print
arXiv:1503.02977v1 fatcat:gal2j5rzdrerdbmcufqpwnvcve
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.
doi:10.1093/imrn/rnw128 fatcat:tvu2gg3i4jhdbi4lbqpvcaxxua
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Kurusch Ebrahimi-Fard, Dominique Manchon, Johannes Singer. "The Hopf Algebra of ($q$-)Multiple Polylogarithms with Non-positive Arguments: Table 1." International mathematics research notices (2016) rnw128