[Le groupe fondamental d'une algèbre triangulaire sans double raccourci]
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 .
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 .
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@article{CRMATH_2005__341_4_211_0,
author = {Le Meur, Patrick},
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},
url = {http://www.numdam.org/articles/10.1016/j.crma.2005.07.004/}
}
TY - JOUR AU - Le Meur, Patrick TI - The fundamental group of a triangular algebra without double bypasses JO - Comptes Rendus. Mathématique PY - 2005 SP - 211 EP - 216 VL - 341 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2005.07.004/ DO - 10.1016/j.crma.2005.07.004 LA - en ID - CRMATH_2005__341_4_211_0 ER -
%0 Journal Article %A Le Meur, Patrick %T The fundamental group of a triangular algebra without double bypasses %J Comptes Rendus. Mathématique %D 2005 %P 211-216 %V 341 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2005.07.004/ %R 10.1016/j.crma.2005.07.004 %G en %F CRMATH_2005__341_4_211_0
Le Meur, Patrick. The fundamental group of a triangular algebra without double bypasses. Comptes Rendus. Mathématique, Tome 341 (2005) no. 4, pp. 211-216. doi : 10.1016/j.crma.2005.07.004. http://www.numdam.org/articles/10.1016/j.crma.2005.07.004/
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