The Hopf Algebra of Formal Multiple Polylogarithms

Abstract We define a Hopf algebra of polylogarithms of an arbitrary field, which is a candidate for a conjectural Hopf algebra of framed mixed Tate motives. Our definition is elementary and mimics Goncharov’s construction of higher Bloch groups. We also discuss the Hodge and motivic realizations of the Hopf algebra of polylogarithms.

Institutions

Max Planck Institute for Mathematics (DE)

Publication Details

Journal: International Mathematics Research Notices
Published: 2025-12-01
DOI: https://doi.org/10.1093/imrn/rnaf361
Primary Topic: Advanced Mathematical Identities
Type: article
Field-Weighted Citation Impact: 0.00

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article

The Hopf Algebra of Formal Multiple Polylogarithms

Dec 1, 2025

International Mathematics Research Notices

Advanced Mathematical Identities

article

The Hopf Algebra of Formal Multiple Polylogarithms

December 1, 2025article en

Abstract

International Mathematics Research NoticesVol. 2026(2)

Max Planck Institute for Mathematics (DE)

Reduced inequalities

Openalex Percentile: Top 14%

Advanced Mathematical Identities

DOI Source OpenAlex

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The Hopf Algebra of Formal Multiple Polylogarithms · International Mathematics Research Notices (2025) | TGRS Research Map | TGRS