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...
| Autores: | , , |
|---|---|
| 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 |
| 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 |
|---|