Three Hopf algebras and their common simplicial and categorical background

We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras of Goncharov for multiple zeta values, that of Connes--Kreimer for renormalization, and a Hopf algebra constructed by Baues to study doub...

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Detalles Bibliográficos
Autores: Gálvez Carrillo, Maria Immaculada|||0000-0002-8338-0437, Kaufmann, Ralph L., Tonks, Andrew
Tipo de recurso: informe técnico
Fecha de publicación:2016
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:2117/102199
Acceso en línea:https://hdl.handle.net/2117/102199
Access Level:acceso abierto
Palabra clave:Hopf algebras
Hopf, Àlgebres de
Classificació AMS::55 Algebraic topology
Àrees temàtiques de la UPC::Matemàtiques i estadística::Topologia::Topologia algebraica
Descripción
Sumario:We consider three a priori totally different setups for Hopf algebras from number theory, mathematical physics and algebraic topology. These are the Hopf algebras 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, cooperads with multiplication and Feynman categories at the ultimate level. These considerations open the door to new constructions and reinterpretation of known constructions in a large common framework