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arXiv · 2203.11588

The Lie coalgebra of multiple polylogarithms

Zachary Greenberg·Dani Kaufman·Haoran Li·Christian K. Zickert
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Abstract

We use Goncharov's coproduct of multiple polylogarithms to define a Lie coalgebra over an arbitrary field. It is generated by symbols subject to inductively defined relations, which we think of as functional relations for multiple polylogarithms. In particular, we have inversion relations and shuffle relations. We relate our definition to Goncharov's Bloch groups, and to the concrete model in weight less than 5 by Goncharov and Rudenko.

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BibTeXRIS

Zachary Greenberg, Dani Kaufman, Haoran Li, Christian K. Zickert. 2022-03-22. The Lie coalgebra of multiple polylogarithms. https://arxiv.org/abs/2203.11588

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