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) Milen YAKIMOV - Lousiana State,
Titre Root of unity quantum cluster algebras
Horaire14:00 à 15:00
RésumeWe will describe a theory of root of unity quantum cluster algebras, which are not necessarily specializations of quantum cluster algebras. All such algebras are shown to be polynomial identity (PI) algebras. Inside each of them, we construct a canonical central subalgebra which is proved to be isomorphic to the underlying cluster algebra. (In turn, this is used to show that two exchange graphs are canonically isomorphic). This setting generalizes the De Concini-Kac-Procesi central subalgebras in big quantum groups and presents a general framework for studying the representation theory of quantum algebras at roots of unity by means of cluster algebras as the relevant data becomes (PI algebra, canonical central subalgebra)=(root of unity quantum cluster algebra, underlying cluster algebra). We also obtain a formula for the corresponding discriminant in this general setting that can be applied in many concrete situations of interest, such as the discriminants of all root of unity quantum unipotent cells for symmetrizable Kac-Moody algebras, defined integrally over Z[root of unity]. This is a joint work with Bach Nguyen (Xavier Univ) and Kurt Trampel (Notre Dame Univ).
Salleà distance / remote