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 : à distance / remote
Adresse :IHP

Depuis le 23 mars 2020, le séminaire se tient à distance. Pour les liens et mots de passe, merci de contacter l'un des organisateurs ou de souscrire à la liste de diffusion https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. L'information nécessaire sera envoyée par courrier électronique peu avant chaque exposé. Les notes et transparents sont disponibles ici.


Since March 23, 2020, the seminar has been taking place remotely. For the links and passwords, please contact one of the organizers or

subscribe to the mailing list at https://listes.math.cnrs.fr/wws/info/paris-algebra-seminar. The connexion information will be emailed shortly before each talk. Slides and notes are available here.


Orateur(s) Osamu IYAMA - Université de Nagoya,
Titre Tilting theory of contracted preprojective algebras and cDV singularities
Horaire14:00 à 15:00

A preprojective algebra of non-Dynkin type has a family of tilting modules associated with the elements in the corresponding Coxeter group W. This family is useful to study the representation theory of the preprojective algebra and also to categorify cluster algebras.
In this talk, I will discuss tilting theory of a contracted preprojective algebra, which is a subalgebra eAe of a preprojective algebra A given by an idempotent e of A. It has a family of tilting modules associated with the chambers in the contracted Tits cone. They correspond bijectively with certain double cosets in W modulo parabolic subgroups. 
I will apply these results to classify a certain family of reflexive modules over a cDV singularities R, called maximal modifying (=MM) modules. We construct an injective map from MM R-modules to tilting modules over a contracted preprojective algebra of extended Dynkin type. This is bijective if R has at worst an isolated singularity. We can recover previous results (Burban-I-Keller-Reiten, I-Wemyss) as a very special case.
This is joint work with Michael Wemyss.

Salleà distance / remote