no. 3
Partial flag varieties and preprojective algebras
[Variétés de drapeaux partiels et algèbres préprojectives]
Geiß, Christof1 ; Leclerc, Bernard2 ; Schröer, Jan3
1 Universidad Nacional Autónoma de México Instituto de Matemáticas 04510 México D.F. (México)
2 Université de Caen LMNO UMR 6139 14032 Caen cedex (France)
3 Universität Bonn Mathematisches Institut Beringstr. 1 53115 Bonn (Germany)
Annales de l'Institut Fourier, Tome 58 (2008) no. 3, pp. 825-876.

Soit Λ 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 Sub Q où Q désigne un Λ-module injectif, et nous introduisons une opération de mutation sur les modules rigides complets de Sub Q. Ceci conduit à des structures d’algèbre amassée sur les anneaux de coordonnées des variétés de drapeaux partiels associées à G.

Let Λ be a preprojective algebra of type A,D,E, and let G be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories Sub Q for Q an injective Λ-module, and we introduce a mutation operation between complete rigid modules in Sub Q. This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to G.

DOI : 10.5802/aif.2371
Classification : 14M15, 16D90, 16G20, 16G70, 17B10, 20G05, 20G20, 20G42
Keywords: Flag variety, preprojective algebra, Frobenius category, rigid module, mutation, cluster algebra, semicanonical basis
Mot clés : variété de drapeaux, algèbre préprojective, catégorie de Frobenius, module rigide, mutation, algèbre amassée, base semi-canonique

Geiß, Christof 1 ; Leclerc, Bernard 2 ; Schröer, Jan 3

1 Universidad Nacional Autónoma de México Instituto de Matemáticas 04510 México D.F. (México)
2 Université de Caen LMNO UMR 6139 14032 Caen cedex (France)
3 Universität Bonn Mathematisches Institut Beringstr. 1 53115 Bonn (Germany) 
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Geiß, Christof; Leclerc, Bernard; Schröer, Jan. Partial flag varieties and preprojective algebras. Annales de l'Institut Fourier, Tome 58 (2008) no. 3, pp. 825-876. doi : 10.5802/aif.2371. https://aif.centre-mersenne.org/articles/10.5802/aif.2371/

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