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Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects

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journal contribution
posted on 08.01.2021, 11:39 by Imma Gálvez-Carrillo, Ralph M Kaufmann, Andrew Tonks
We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebra of Goncharov for multiple zeta values, that of Connes-Kreimer for renormalization, and a Hopf algebra constructed by Baues to study double loop spaces. We show that these examples can be successively unified by considering simplicial objects, co-operads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretations of known constructions in a large common framework, which is presented step-by-step with examples throughout. In this first part of two papers, we concentrate on the simplicial and operadic aspects.

History

Citation

Communications in Number Theory and Physics Volume 14 (2020), Number 1, pp. 1-90

Author affiliation

Department of Mathematics

Version

AM (Accepted Manuscript)

Published in

Communications in Number Theory and Physics

Volume

14

Issue

1

Pagination

1 - 90

Publisher

International Press of Boston

issn

1931-4523

eissn

1931-4531

Copyright date

2020

Notes

This replacement is part I of the final version of the paper, which has been split into two parts. The second part is available from the arXiv under the title "Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation" arXiv:2001.08722

Language

en

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