Nous construisons une suite exacte longue, exprimant les modules d'extension d'une algèbre triangulaire en fonctions de ceux associés aux algèbres de sa diagonale, dans deux cas : soit son bimodule est un module-à-gauche projectif soit c'est un module-à-droite plat. Ceci complète un résultat de Palmér et Roos sur la dimension globale des algèbres triangulaires.
We construct a long exact sequence where the extensions modules of a triangular algebra are involved with extension modules of its diagonal algebras. This holds in two cases: either its bimodule is right-projective or it is left-flat. This completes a result of Palmér and Roos about the global dimension of triangular algebras.
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@article{CRMATH_2004__339_6_387_0,
author = {Belkacem Bendiffalah},
title = {Modules d'extensions des alg\`ebres triangulaires},
journal = {Comptes Rendus. Math\'ematique},
pages = {387--390},
publisher = {Elsevier},
volume = {339},
number = {6},
year = {2004},
doi = {10.1016/j.crma.2004.07.007},
language = {fr},
}
Belkacem Bendiffalah. Modules d'extensions des algèbres triangulaires. Comptes Rendus. Mathématique, Volume 339 (2004) no. 6, pp. 387-390. doi : 10.1016/j.crma.2004.07.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.07.007/
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