Séminaire de Mathématique

Hopf algebras from Feynman categories

par Ralph Kaufmann (Purdue University & IHES)

Europe/Paris
Amphithéâtre Léon Motchane (IHES)

Amphithéâtre Léon Motchane

IHES

Le Bois Marie 35, route de Chartres 91440 Bures-sur-Yvette
Description
 
We introduce Feynman categories and show that they naturally define bi-algebras. In good circumstances these bi-algebras have Hopf quotients. Corresponding to several levels of sophistication and decoration (both terms have technical definitions), we recover the Hopf algebras of Goncharov and Brown from number theory, a Hopf algebra of Baues used in the analysis of double loop spaces and the various Hopf algebras of Connes-Kreimer used in QFT as examples of the general theory. Co-actions also appear naturally in this context as we will explain.
Organisé par

Maxim Kontsevich

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