hereditary Artin algebras — 1 articles found.

The global dimension of the endomorphism ring of a generator-cogenerator for a hereditary Artin algebra

C. R. Math. Rep. Acad. Sci. Canada Vol. 30 (3) 2008, pp. 89–96
Vol.30 (3) 2008
Vlastimil Dlab; Claus Michael Ringel Details
(Received: 2008-03-07 )
(Received: 2008-03-07 )

Vlastimil Dlab, School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6; email: dlab@math.carleton.ca

Claus Michael Ringel, Fakultat fur Universitat Bielefeld, D-33 501 Bielefeld, Germany; email: ringel@math.uni-bielefeld.de

Abstract/Résumé:

Let \( \Lambda\) be a hereditary Artin algebra and \( M\) a \( \Lambda\)-module that is both a generator and a cogenerator. We are going to describe the possibilities for the global dimension of \( \textrm{End}(M)\) in terms of the cardinalities of the Auslander–Reiten orbits of indecomposable \( \Lambda\)-modules.

Soit \( \Lambda\) une algèbre d’Artin héréditaire et \( M\) un \( \Lambda\)-module qui est un générateur-cogénérateur. Nous allons décrire toutes les possibilités pour la dimension globale de \( \textrm{End}(M)\) à l’aide des cardinalités des orbites d’Auslander–Reiten des \( \Lambda\)-modules indécomposables.

Keywords: hereditary Artin algebras, representation dimension

AMS Subject Classification: Homological dimension 16E10

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