On généralise au cas non simplement lacé des résultats de Geiß, Leclerc et Schröer sur les structures amassées des algèbres de fonctions sur les sous-groupes unipotents maximaux des groupes de Lie simples. Cela permet en particulier de voir les structures amassées dans le cas non simplement lacé comme projections des structures amassées dans le cas simplement lacé. Cela permet aussi de montrer la liberté des monômes d'amas dans le cas non simplement lacé.
We generalize to the non simply-laced case results of Geiß, Leclerc and Schröer about the cluster structure of the coordinate ring of the maximal unipotent subgroups of simple Lie groups. In this way, cluster structures in the non simply-laced case can be seen as projections of cluster structures in the simply-laced case. This allows us to prove that cluster monomials are linearly independent in the non simply-laced case.
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@article{CRMATH_2008__346_7-8_379_0,
author = {Demonet, Laurent},
title = {Alg\`ebres amass\'ees et alg\`ebres pr\'eprojectives : le cas non simplement lac\'e},
journal = {Comptes Rendus. Math\'ematique},
pages = {379--384},
publisher = {Elsevier},
volume = {346},
number = {7-8},
year = {2008},
doi = {10.1016/j.crma.2008.02.007},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.02.007/}
}
TY - JOUR AU - Demonet, Laurent TI - Algèbres amassées et algèbres préprojectives : le cas non simplement lacé JO - Comptes Rendus. Mathématique PY - 2008 SP - 379 EP - 384 VL - 346 IS - 7-8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.02.007/ DO - 10.1016/j.crma.2008.02.007 LA - fr ID - CRMATH_2008__346_7-8_379_0 ER -
%0 Journal Article %A Demonet, Laurent %T Algèbres amassées et algèbres préprojectives : le cas non simplement lacé %J Comptes Rendus. Mathématique %D 2008 %P 379-384 %V 346 %N 7-8 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.02.007/ %R 10.1016/j.crma.2008.02.007 %G fr %F CRMATH_2008__346_7-8_379_0
Demonet, Laurent. Algèbres amassées et algèbres préprojectives : le cas non simplement lacé. Comptes Rendus. Mathématique, Tome 346 (2008) no. 7-8, pp. 379-384. doi : 10.1016/j.crma.2008.02.007. http://www.numdam.org/articles/10.1016/j.crma.2008.02.007/
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