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Christof Geiß; Bernard Leclerc; Jan Schröer
Partial flag varieties and preprojective algebras
(Variétés de drapeaux partiels et algèbres préprojectives)
Annales de l'institut Fourier, 58 no. 3 (2008), p. 825-876, doi: 10.5802/aif.2371
Article PDF | Analyses MR 2427512 | Zbl 1151.16009 | 1 citation dans Cedram
Class. Math.: 14M15, 16D90, 16G20, 16G70, 17B10, 20G05, 20G20, 20G42
Mots clés: variété de drapeaux, algèbre préprojective, catégorie de Frobenius, module rigide, mutation, algèbre amassée, base semi-canonique

Résumé - Abstract

Soit $\Lambda $ une algèbre préprojective de type $A, D, E$, et soit $G$ le groupe algébrique complexe semi-simple et simplement connexe correspondant. Nous étudions les modules rigides des sous-catégories ${\rm Sub\,} Q$ où $Q$ désigne un $\Lambda $-module injectif, et nous introduisons une opération de mutation sur les modules rigides complets de ${\rm Sub\,} Q$. Ceci conduit à des structures d’algèbre amassée sur les anneaux de coordonnées des variétés de drapeaux partiels associées à $G$.

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