The Gabriel-Roiter measure
Ringel CM (2005)
Bulletin des Sciences Mathématiques 129(9): 726-748.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Einrichtung
Abstract / Bemerkung
The first Brauer-Thrall conjecture asserts that algebras of bounded representation type have finite representation type. This conjecture was solved by Roiter in 1968. The induction scheme which he used in his proof prompted Gabriel to introduce an invariant which we propose to call Gabriel-Roiter,measure. This invariant is defined for any finite length module and it will be studied in detail in this paper. Whereas Roiter and Gabriel were dealing with algebras of bounded representation type only, it is the purpose of the present paper to demonstrate the relevance of the Gabriel-Roiter measure for algebras in general, in particular for those of infinite representation type. (c) 2005 Elsevier SAS. All rights reserved.
Stichworte
infinite length modules;
Brauer-Thrall conjectures;
Gabriel-Roiter;
measure;
Gabriel-Roiter inclusion;
Gabriel-Roiter filtration;
preprojective modules;
preinjective modules;
kronecker quiver;
comeasure;
rhombic picture;
finite length modules;
artin algebra;
indecomposable representations
Erscheinungsjahr
2005
Zeitschriftentitel
Bulletin des Sciences Mathématiques
Band
129
Ausgabe
9
Seite(n)
726-748
ISSN
0007-4497
Page URI
https://pub.uni-bielefeld.de/record/1601896
Zitieren
Ringel CM. The Gabriel-Roiter measure. Bulletin des Sciences Mathématiques. 2005;129(9):726-748.
Ringel, C. M. (2005). The Gabriel-Roiter measure. Bulletin des Sciences Mathématiques, 129(9), 726-748. https://doi.org/10.1016/j.bulsci.2005.04.002
Ringel, Claus Michael. 2005. “The Gabriel-Roiter measure”. Bulletin des Sciences Mathématiques 129 (9): 726-748.
Ringel, C. M. (2005). The Gabriel-Roiter measure. Bulletin des Sciences Mathématiques 129, 726-748.
Ringel, C.M., 2005. The Gabriel-Roiter measure. Bulletin des Sciences Mathématiques, 129(9), p 726-748.
C.M. Ringel, “The Gabriel-Roiter measure”, Bulletin des Sciences Mathématiques, vol. 129, 2005, pp. 726-748.
Ringel, C.M.: The Gabriel-Roiter measure. Bulletin des Sciences Mathématiques. 129, 726-748 (2005).
Ringel, Claus Michael. “The Gabriel-Roiter measure”. Bulletin des Sciences Mathématiques 129.9 (2005): 726-748.
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