Let A be a basic connected finite dimensional algebra over a field of characteristic zero. A fundamental group depending on the presentation of A has been defined by several authors [see R. Martínez-Villa, J.A. de La Peña, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (1983) 277–292]. Assuming the quiver of A has no oriented cycles and no double bypasses, we show there exists a suitable presentation of A with quiver and admissible relations, with fundamental group denoted by , such that the fundamental group of any other presentation of A with quiver and admissible relations is a quotient of .
Soit A une algèbre basique connexe et de dimension finie sur un corps de caractéristique nulle. Plusieurs auteurs [voir R. Martínez-Villa, J.A. de La Peña, The universal cover of a quiver with relations, J. Pure Appl. Algebra 30 (1983) 277–292] ont défini pour A un groupe fondamental dépendant du choix d'une présentation de A. En supposant que le carquois de A n'a pas de cycle orienté et n'a pas de double raccourci, nous démontrons qu'il existe une présentation privilégiée de A par carquois et relations admissibles, de groupe fondamental noté , telle que le groupe fondamental de toute autre présentation de A par carquois et relations admissibles est un quotient de .
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Patrick Le Meur 1
@article{CRMATH_2005__341_4_211_0, author = {Patrick Le Meur}, title = {The fundamental group of a triangular algebra without double bypasses}, journal = {Comptes Rendus. Math\'ematique}, pages = {211--216}, publisher = {Elsevier}, volume = {341}, number = {4}, year = {2005}, doi = {10.1016/j.crma.2005.07.004}, language = {en}, }
Patrick Le Meur. The fundamental group of a triangular algebra without double bypasses. Comptes Rendus. Mathématique, Volume 341 (2005) no. 4, pp. 211-216. doi : 10.1016/j.crma.2005.07.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.07.004/
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