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arXiv · 2001.08722

Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation

Imma Gálvez-Carrillo·Ralph M. Kaufmann·Andrew Tonks
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Abstract

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.

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BibTeXRIS

Imma Gálvez-Carrillo, Ralph M. Kaufmann, Andrew Tonks. 2020-01-23. Three Hopf algebras from number theory, physics & topology, and their common background II: general categorical formulation. https://doi.org/10.4310/cntp.2020.v14.n1.a2

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