Michaël Mignard

par M. Michaël Mignard

jeudi 14 févr. 2019, 14:15 → 15:15 Europe/Paris

318 (IMB)

G-graded vector spaces and classification problems (part I)

 

The context of this talk is the one of tensor categories. Those are very abstract algebraic structures related to many other areas of both mathematics and physics. Among them, the more particular cases of fusion and modular categories -and classification problems of those structures- are of interest. It is not the ambition of this talk to give a general survey on fusion categories, but rather to give  an insight of those structures by the study of a toy example linked with finite groups. In that perspective, after an introdution that will show the general picture of the classification problems we will discuss, we will recall some definitions and results about (finite) groups, their representations and tensor product of vector spaces. Then we will introduce the notion of G-graded spaces, our principal object of study, and its link with cohomology of groups. Finally we will explain the description of the so-called center of G-graded vector spaces, which will be essential in the comprehension of our problems. This talk will thus essentially be a description of the objects we want to study, a second part about actual classification results can be scheduled later.