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

Author
Galvez, M.; Kaufmann, R.M.; Tonks, A.
Type of activity
Journal article
Journal
Communications in Number Theory and Physics
Date of publication
2020-01-01
Volume
14
Number
1
First page
1
Last page
90
DOI
10.4310/CNTP.2020.v14.n1.a1
Project funding
GEOMETRIA DE VRIETATS I APLICACIONS (GEOMVAP)
Geomatría algebraica, simpléctica, aritmética y aplicaciones.
Geometria de varietats i aplicacions
Geometry and topology of varieties, algebra and applications
Repository
http://hdl.handle.net/2117/180029 Open in new window
https://arxiv.org/abs/1607.00196 Open in new window
URL
https://www.intlpress.com/site/pub/pages/journals/items/cntp/content/vols/0014/0001/a001/index.php Open in new window
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 consideratio...
Citation
Galvez, M.; Kaufmann, R.M.; Tonks, A. Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects. "Communications in Number Theory and Physics", 1 Gener 2020, vol. 14, núm. 1, p. 1-90.
Keywords
Algebraic Geometry, Algebraic Topology, Category Theory, High Energy Physics - Theory, Mathematical Physics
Group of research
GEOMVAP - Geometry of Manifolds and Applications

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