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) Andrea PASCUAL - Uppsala,
Titre Self-injective Jacobian algebras from Postnikov diagrams
Horaire14:00 à 15:00
RésumeA Postnikov diagram is a collection of curves in a disk subject to some axioms depending on two integers $1\leq k\leq n$. The arising combinatorics is related to that of the cluster structure of the coordinate ring of the Grassmannian of $k$-subspaces of $\mathbb C^n$. To a Postnikov diagram one can associate a finite-dimensional Jacobian algebra, by work of Oh-Postnikov-Speyer. Baur-King-Marsh later proved that the Jacobian algebra is isomorphic to the stable endomorphism algebra of a cluster tilting object in a 2-Calabi-Yau category introduced by Jensen-King-Su. In this talk I will explain how to characterise self-injectivity of this Jacobian algebra combinatorially. I will also show some new examples of planar self-injective quivers with potential one gets in this way (the terminology is that of Herschend-Iyama), and explain a connection to 2-dimensional Auslander-Reiten theory.