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) Dan KAPLAN - ,
Titre Multiplicative preprojective algebras for Dynkin quivers
Horaire14:00 à 15:00
RésumeCrawley-Boevey and Shaw defined the multiplicative preprojective algebra to understand Kac’s middle convolution and to solve the Deligne-Simpson problem. In Shaw’s thesis he noticed a curious phenomenon: for the D_4 quiver the multiplicative preprojective algebra (with parameter q=1) is isomorphic to the (additive) preprojective algebra if and only if the underlying field has characteristic not two. Later, Crawley-Boevey proved the multiplicative and additive preprojective algebras are isomorphic for all Dynkin quivers over the complex numbers. Recent work of Etgü-Lekili and Lekili-Ueda, in the dg-setting, sharpens the result to hold over fields of good characteristic, meaning characteristic not 2 in type D, not 2 or 3 in type E and not 2, 3, or 5 for E_8. Neither work produces an isomorphism. In this talk, I will explain how to construct these isomorphisms and prove their non-existence in the bad (i.e., not good) characteristics. For each bad characteristic, a single class in zeroth Hochschild homology obstructs the existence of an isomorphism. Time permitting, I’ll explain how to interpret these results in the dg-setting where the 2-Calabi-Yau property allows us to recast these obstructions as non-trivial deformations, using Van den Bergh duality.
Salleà distance / remote