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...
| Autores: | , , |
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| 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 |
| Sumario: | 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 |
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