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 for L(F)≤4 by Goncharov and Rudenko.

Original languageEnglish
JournalJournal of Algebra
Volume645
Pages (from-to)164-182
ISSN0021-8693
DOIs
Publication statusPublished - 2024

Keywords

  • Bloch groups
  • Motivic Lie coalgebra
  • Multiple polylogarithms
  • Polylogarithm relations
  • Symbols

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