The Hopf algebra of formal multiple polylogarithms
Steven Charlton, Andrei Matveiakin, Danylo Radchenko, Daniil Rudenko
TL;DR
This paper introduces a Hopf algebra structure for formal multiple polylogarithms over any field, aiming to connect with the conjectural algebra of mixed Tate motives, and explores its realizations.
Contribution
It provides an elementary construction of a Hopf algebra of polylogarithms that parallels Goncharov's higher Bloch groups, advancing the algebraic understanding of polylogarithms.
Findings
Defines a Hopf algebra of polylogarithms for any field.
Connects the algebra to conjectural mixed Tate motives.
Discusses Hodge and motivic realizations of the algebra.
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.
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Taxonomy
TopicsMolecular spectroscopy and chirality · Advanced Mathematical Identities · Advanced Algebra and Logic