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

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...

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Detalles Bibliográficos
Autores: Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437, Kaufmann, Ralph M., Tonks, Andrew
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/180029
Acceso en línea:https://hdl.handle.net/2117/180029
https://dx.doi.org/10.4310/CNTP.2020.v14.n1.a1
Access Level:acceso abierto
Palabra clave:Hopf algebras
Algebraic Topology
High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Category Theory
Hopf, Àlgebres de
Classificació AMS::55 Algebraic topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
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spelling Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspectsGálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437Kaufmann, Ralph M.Tonks, AndrewHopf algebrasAlgebraic TopologyHigh Energy Physics - TheoryMathematical PhysicsAlgebraic GeometryCategory TheoryHopf, Àlgebres deClassificació AMS::55 Algebraic topologyÀrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraicaWe 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 aspectsPeer Reviewed20202020-01-0120202020-03-16journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/180029https://dx.doi.org/10.4310/CNTP.2020.v14.n1.a1reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2015-69135-P GEOMETRIA Y TOPOLOGIA DE VARIEDADES, ALGEBRA Y APLICACIONESMinisterio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2012-38122-C03-01 GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1800292026-05-27T15:37:01Z
dc.title.none.fl_str_mv Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
title Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
spellingShingle Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Hopf algebras
Algebraic Topology
High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Category Theory
Hopf, Àlgebres de
Classificació AMS::55 Algebraic topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
title_short Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
title_full Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
title_fullStr Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
title_full_unstemmed Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
title_sort Three Hopf algebras from number theory, physics & topology, and their common background I: operadic & simplicial aspects
dc.creator.none.fl_str_mv Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Kaufmann, Ralph M.
Tonks, Andrew
author Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
author_facet Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437
Kaufmann, Ralph M.
Tonks, Andrew
author_role author
author2 Kaufmann, Ralph M.
Tonks, Andrew
author2_role author
author
dc.subject.none.fl_str_mv Hopf algebras
Algebraic Topology
High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Category Theory
Hopf, Àlgebres de
Classificació AMS::55 Algebraic topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
topic Hopf algebras
Algebraic Topology
High Energy Physics - Theory
Mathematical Physics
Algebraic Geometry
Category Theory
Hopf, Àlgebres de
Classificació AMS::55 Algebraic topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
description 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
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
2020
2020-03-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/180029
https://dx.doi.org/10.4310/CNTP.2020.v14.n1.a1
url https://hdl.handle.net/2117/180029
https://dx.doi.org/10.4310/CNTP.2020.v14.n1.a1
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2015-69135-P GEOMETRIA Y TOPOLOGIA DE VARIEDADES, ALGEBRA Y APLICACIONES
Ministerio de Economía y Competitividad http://doi.org/10.13039/501100003329 MTM2012-38122-C03-01 GEOMATRIA ALGEBRAICA, SIMPLECTICA, ARITMETICA Y APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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