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Comptes Rendus Mathématique
Volume 341, n° 4
pages 211-216 (août 2005)
Doi : 10.1016/j.crma.2005.07.004
Received : 16 Mars 2005 ;  accepted : 28 June 2005
The fundamental group of a triangular algebra without double bypasses
Le groupe fondamental dʼune algèbre triangulaire sans double raccourci
 

Patrick Le Meur
Institut de mathématiques et de modélisation de Montpellier, UMR CNRS 5149, université Montpellier 2, case courier 051, place Eugène-Bataillon, 34095 Montpellier cedex 5, France 

Abstract

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  . To cite this article: P. Le Meur, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.
Résumé

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 dʼune présentation de A . En supposant que le carquois de A nʼa pas de cycle orienté et nʼa pas de double raccourci, nous démontrons quʼil 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  . Pour citer cet article : P. Le Meur, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.


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