Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation
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: | , , |
|---|---|
| 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:2117/180271 |
| Acceso en línea: | https://hdl.handle.net/2117/180271 https://dx.doi.org/10.4310/CNTP.2020.v14.n1.a2 |
| Access Level: | acceso abierto |
| Palabra clave: | Hopf algebras Algebraic Topology Mathematical Physics Category Theory Number Theory Quantum Algebra Hopf, Àlgebres de 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 second part of two papers, we give the general categorical formulation |
|---|