Symmetril Moulds, Generic Group Schemes, Resummation of Mzvs
Claudia Malvenuto (Sapienza University of Rome), Fr\'ed\'eric Patras, (JAD)
TL;DR
This paper explores the algebraic structures and resummation techniques related to multiple zeta values (MZVs), inspired by Ecalle's mould calculus, introducing a Hopf algebra encoding and a novel resummation method.
Contribution
It introduces a Hopf algebra framework for symmetril moulds and a new resummation process for MZVs, advancing the algebraic understanding of these values.
Findings
Developed a Hopf algebra encoding for symmetril moulds
Proposed a new resummation technique for MZVs
Connected mould calculus with algebraic structures of MZVs
Abstract
The present article deals with various generating series and group schemes (not necessarily affine ones) associated with MZVs. Our developments are motivated by Ecalle's mould calculus approach to the latter. We propose in particular a Hopf algebra--type encoding of symmetril moulds and introduce a new resummation process for MZVs.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Homotopy and Cohomology in Algebraic Topology