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
Description

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) Baptiste ROGNERUD - Université de Paris,
Titre Combinatorics of quasi-hereditary structures, I
Date08/06/2020
Horaire14:00 à 14:30
Diffusion
Résume

Quasi-hereditary algebras were introduced by Cline, Parshall and Scott as a tool to study highest weight theories which arise in the representation theories of semi-simple complex Lie algebras and reductive groups. Surprisingly, there are now many examples of such algebras, such as Schur algebras, algebras of global dimension at most two, incidence algebras and many more. 

A quasi-hereditary algebra is an Artin algebra together with a partial order on its set of isomorphism classes of simple modules which satisfies certain conditions. In the early examples the partial order predated (and motivated) the theory, so the choice was clear. However, there are instances of quasi-hereditary algebras where there is no natural choice for the partial ordering and even if there is such a natural choice, one may wonder about all the possible orderings.

In this talk we will explain that all these choices for an algebra $A$ can be organized in a finite partial order which is in relation with the tilting theory of $A$. In a second part of the talk we will focus on the case where $A$ is the path algebra of a Dynkin quiver.

Salleà distance / remote
AdresseIHP
© IMJ-PRG