Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation
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arXiv
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| Format: | Preprint |
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2020
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| author | Gálvez-Carrillo, Imma Kaufmann, Ralph M. Tonks, Andrew |
| author_facet | Gálvez-Carrillo, Imma Kaufmann, Ralph M. Tonks, Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_08722 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation Gálvez-Carrillo, Imma Kaufmann, Ralph M. Tonks, Andrew Algebraic Topology Mathematical Physics Category Theory Number Theory Quantum Algebra 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. |
| title | Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation |
| topic | Algebraic Topology Mathematical Physics Category Theory Number Theory Quantum Algebra |
| url | https://arxiv.org/abs/2001.08722 |