Indecomposable representations of the Kronecker quivers

Ringel CM (2013)
Proceedings of the American Mathematical Society 141(1): 115-121.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Let k be a field and Lambda the n-Kronecker algebra. This is the path algebra of the quiver with 2 vertices, a source and a sink, and n arrows from the source to the sink. It is well known that the dimension vectors of the indecomposable Lambda-modules are the positive roots of the corresponding Kac-Moody algebra. Thorsten Weist has shown that for every positive root there are tree modules with this dimension vector and that for every positive imaginary root there are at least n tree modules. Here, we present a short proof of this result. The considerations used also provide a calculation-free proof that all exceptional modules over the path algebra of a finite quiver are tree modules.
Erscheinungsjahr
2013
Zeitschriftentitel
Proceedings of the American Mathematical Society
Band
141
Ausgabe
1
Seite(n)
115-121
ISSN
0002-9939
Page URI
https://pub.uni-bielefeld.de/record/2638624

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Ringel CM. Indecomposable representations of the Kronecker quivers. Proceedings of the American Mathematical Society. 2013;141(1):115-121.
Ringel, C. M. (2013). Indecomposable representations of the Kronecker quivers. Proceedings of the American Mathematical Society, 141(1), 115-121. doi:10.1090/S0002-9939-2012-11296-1
Ringel, C. M. (2013). Indecomposable representations of the Kronecker quivers. Proceedings of the American Mathematical Society 141, 115-121.
Ringel, C.M., 2013. Indecomposable representations of the Kronecker quivers. Proceedings of the American Mathematical Society, 141(1), p 115-121.
C.M. Ringel, “Indecomposable representations of the Kronecker quivers”, Proceedings of the American Mathematical Society, vol. 141, 2013, pp. 115-121.
Ringel, C.M.: Indecomposable representations of the Kronecker quivers. Proceedings of the American Mathematical Society. 141, 115-121 (2013).
Ringel, Claus Michael. “Indecomposable representations of the Kronecker quivers”. Proceedings of the American Mathematical Society 141.1 (2013): 115-121.

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