# 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 , David Hernandez , Bernhard Keller , Thierry Levasseur , Sophie Morier-Genoud Salle : Zoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar Adresse : Zoom ou IHP Salle 01 Description 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) Sota Asai - , Titre TF equivalence classes and canonical decompositions for E-tame algebras Date 31/10/2022 Horaire 14:00 à 15:00 Diffusion Résume This is joint work with Osamu Iyama. Let $A$ be a finite dimensional algebra over an algebraically closed field. Then the numerical torsion pairs of Baumann-Kamnitzer-Tingley give an equivalence relation on the real Grothendieck group of finitely generated projective $A$-modules, which is called TF equivalence. By results of Yurikusa and Bruestle-Smith-Treffinger, we have that the g-vector cone of each 2-term presilting complex is a TF equivalence class. To get more TF equivalence classes, we can use canonical decompositions of elements in the (integral) Grothendieck group of finitely generated projectives introduced by Derksen-Fei. We have showed that the cone defined by the canonical decomposition of each element is contained in some single TF equivalence class. Moreover, we have also obtained that, if $A$ is an E-tame algebra, then this cone is precisely a TF equivalence class. In this talk, I will explain these results and some important steps to prove them. Salle Zoom ou hybride selon les orateurs. Info sur https://researchseminars.org/seminar/paris-algebra-seminar Adresse Zoom ou IHP Salle 01