English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

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

MPS-Authors
/persons/resource/persons235544

Kaufmann,  Ralph M.
Max Planck Institute for Mathematics, Max Planck Society;

Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)
There are no public fulltexts stored in PuRe
Supplementary Material (public)
There is no public supplementary material available
Citation

Gálvez-Carrillo, I., Kaufmann, R. M., & Tonks, A. (2020). Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects. Communications in Number Theory and Physics, 14(1), 1-90. doi:10.4310/CNTP.2020.v14.n1.a1.


Cite as: https://hdl.handle.net/21.11116/0000-0006-0522-E
Abstract
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.