Let be a preprojective algebra of type , and let be the corresponding semisimple simply connected complex algebraic group. We study rigid modules in subcategories for an injective -module, and we introduce a mutation operation between complete rigid modules in . This yields cluster algebra structures on the coordinate rings of the partial flag varieties attached to .
Soit une algèbre préprojective de type , et soit le groupe algébrique complexe semi-simple et simplement connexe correspondant. Nous étudions les modules rigides des sous-catégories où désigne un -module injectif, et nous introduisons une opération de mutation sur les modules rigides complets de . Ceci conduit à des structures d’algèbre amassée sur les anneaux de coordonnées des variétés de drapeaux partiels associées à .
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
@article{AIF_2008__58_3_825_0, author = {Gei{\ss}, Christof and Leclerc, Bernard and Schr\"oer, Jan}, title = {Partial flag varieties and preprojective algebras}, journal = {Annales de l'Institut Fourier}, pages = {825--876}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {3}, year = {2008}, doi = {10.5802/aif.2371}, zbl = {1151.16009}, mrnumber = {2427512}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2371/} }
TY - JOUR AU - Geiß, Christof AU - Leclerc, Bernard AU - Schröer, Jan TI - Partial flag varieties and preprojective algebras JO - Annales de l'Institut Fourier PY - 2008 SP - 825 EP - 876 VL - 58 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2371/ DO - 10.5802/aif.2371 LA - en ID - AIF_2008__58_3_825_0 ER -
%0 Journal Article %A Geiß, Christof %A Leclerc, Bernard %A Schröer, Jan %T Partial flag varieties and preprojective algebras %J Annales de l'Institut Fourier %D 2008 %P 825-876 %V 58 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2371/ %R 10.5802/aif.2371 %G en %F AIF_2008__58_3_825_0
Geiß, Christof; Leclerc, Bernard; Schröer, Jan. Partial flag varieties and preprojective algebras. Annales de l'Institut Fourier, Volume 58 (2008) no. 3, pp. 825-876. doi : 10.5802/aif.2371. http://archive.numdam.org/articles/10.5802/aif.2371/
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