A ug 2 00 7 Partial flag varieties and preprojective algebras
نویسندگان
چکیده
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. Résumé Soit Λ une algèbre préprojective de type A, D, E, et soit G le groupe algébrique complexe semi-simple et simplement connexe correspondant. Nousétudions les modules rigides des sous-catégories Sub Q o` u Q désigne un Λ-module injectif, et nous introduisons une opération de mutation sur les modules rigides complets de Sub Q. Ceci conduità des structures d'algèbre amassée sur les anneaux de coordonnées des variétés de drapeaux partiels associéesà G.
منابع مشابه
5 N ov 2 00 6 Partial flag varieties and preprojective algebras
Let Λ be a preprojective algebra of Dynkin type, and let G be the corresponding semisim-ple 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.
متن کامل5 S ep 2 00 6 Partial flag varieties and preprojective algebras
Let Λ be a preprojective algebra of Dynkin type, and let G be the corresponding complex semisimple simply connected 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.
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