Cluster-concealed algebras

Ringel CM (2011)
Advances in Mathematics 226(2): 1513-1537.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
The cluster-tilted algebras have been introduced by Buan, Marsh and Reiten, they are the endomorphism rings of cluster-tilting objects T in cluster categories; we call such an algebra cluster-concealed in case T is obtained from a preprojective tilting module. For example, all representation-finite cluster-tilted algebras are cluster-concealed. If C is a representation-finite cluster-tilted algebra, then the indecomposable C-modules are shown to be determined by their dimension vectors. For a general cluster-tilted algebra C, we are going to describe the dimension vectors of the indecomposable C-modules in terms of the root system of a quadratic form. The roots may have both positive and negative coordinates and we have to take absolute values. (C) 2010 Elsevier Inc. All rights reserved.
Stichworte
Torsion pairs; Matrix categories; Concealed algebras; Root system; Dimension vectors; Finite representation type; Cluster-tilted algebras
Erscheinungsjahr
2011
Zeitschriftentitel
Advances in Mathematics
Band
226
Ausgabe
2
Seite(n)
1513-1537
ISSN
0001-8708
Page URI
https://pub.uni-bielefeld.de/record/1968146

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Ringel CM. Cluster-concealed algebras. Advances in Mathematics. 2011;226(2):1513-1537.
Ringel, C. M. (2011). Cluster-concealed algebras. Advances in Mathematics, 226(2), 1513-1537. doi:10.1016/j.aim.2010.08.014
Ringel, C. M. (2011). Cluster-concealed algebras. Advances in Mathematics 226, 1513-1537.
Ringel, C.M., 2011. Cluster-concealed algebras. Advances in Mathematics, 226(2), p 1513-1537.
C.M. Ringel, “Cluster-concealed algebras”, Advances in Mathematics, vol. 226, 2011, pp. 1513-1537.
Ringel, C.M.: Cluster-concealed algebras. Advances in Mathematics. 226, 1513-1537 (2011).
Ringel, Claus Michael. “Cluster-concealed algebras”. Advances in Mathematics 226.2 (2011): 1513-1537.