Séminaires : Séminaire d'Algèbre

Equipe(s) : gr,
Responsables :J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud.
Email des responsables : Jacques Alev <jacques.alev@univ-reims.fr>, David Hernandez <david.hernandez@imj-prg.fr>, Bernhard Keller <bernhard.keller@imj-prg.fr>, Thierry Levasseur <Thierry.Levasseur@univ-brest.fr>, Sophie Morier-Genoud <sophie.morier-genoud@imj-prg.fr>
Salle : 001
Adresse :IHP


Orateur(s) Ehud MEIR - IHES,
Titre On module categories over graded fusion categories
Horaire14:30 à 15:30
RésumeFusion categories arise in several areas of mathematics- such as the representation theory of Hopf algebras and topological quantum field theory. They are tensor categories which satisfy certain rigidity assumptions- they are semisimple, have a finite number of simple objects, and they have duals. A general classification of fusion categories seems to be out of reach at the moment. However, Etingof Nikshych and Ostrik have classified all fusion categories which are extensions of a given fusion category by a given finite group $G$, by cohomological machinery (these are categories which are naturally graded by the group $G$) In this talk I will describe a joint work with Evgeny Musicantov, about the classification of module categories (which, in this setting, are the categorical analogues of modules over a ring) over these fusion categories. I will explain all the fundamental notions, their relevance for the theory of Hopf algebras, and the role that the cohomological machinery plays in the classification.