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 : Info sur https://researchseminars.org/seminar/paris-algebra-seminar
Adresse :

Le séminaire est prévu en présence à l'IHP et 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) Leonid Positselski - ,
Titre The homomorphism removal and repackaging construction
Horaire14:15 à 15:15

This work is an attempt to understand the maximal natural generality context for the Koenig-Kuelshammer-Ovsienko construction in the theory of quasi-hereditary algebras by putting it into a category-theoretic context. Given a field k and a k-linear exact category E with a chosen set of nonzero objects F_i such that every object of E is a finitely iterated extension of some F_i, we construct a coalgebra C whose irreducible comodules L_i are indexed by the same indexing set, and an exact functor from C-comod to E taking L_i to F_i such that the spaces Ext^n between L_i in C−comod are the same as between F_i in E (for n > 0). Thus, the abelian category C−comod is obtained from the exact category E by removing all the nontrivial homomorphisms between the chosen objects F_i in E while keeping the Ext spaces unchanged. The removed homomorphisms are then repackaged into a semialgebra S over C such that the exact category E can be recovered as the category of S-semimodules induced from finite-dimensional C-comodules. The construction used Koszul duality twice: once as absolute and once as relative Koszul duality.

Talk shared by the GAP conference, cfhttps://personal.psu.edu/mps16/hirsutes2023/gap2023.html

You can follow the talk using the link (without interaction): https://www.ihp.fr/fr/live-0