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 : 001
Adresse :IHP


Orateur(s) Geoffrey Janssens - Bruxelles VUB,
Titre A Reduction theorem for tau-rigid modules : string algebras ringing
Horaire14:00 à 15:00
Motivated by (mutation) deficiencies in classical tilting theory, Adachi, Iyama and Reiten introduced the theory of support tau-tilting modules. In this talk we will be concerned with the problem of determining all support tau-tilting modules (or equivalently all basic two-term silting complexes) for various finite dimensional algebras A over an algebraically closed field. To this end, I will explain a tool that allows to reduce the problem for a given algebra to a more tractable one by repeatedly taking quotients by central elements (in the radical). In practice, it turns out that this process often spits out a string algebra for which I will present an explicit combinatorial description of the support tau-tilting modules. Also various applications, such as tau-tilting finiteness and iterated tilting mutation, to blocks of group algebras and special biserial algebras will be presented.  This is based on joint work with Florian Eisele and Theo Raedschelders.