Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 507-523 |
| Seitenumfang | 17 |
| Fachzeitschrift | Journal of algebraic combinatorics |
| Jahrgang | 34 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - Nov. 2011 |
Abstract
We give a complete classification of torsion pairs in the cluster category of Dynkin type A n . Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng ( 1005.4364v1 [math.RT, 2010). This allows us to count the number of torsion pairs in the cluster category of type A n . We also count torsion pairs up to Auslander-Reiten translation.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
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in: Journal of algebraic combinatorics, Jahrgang 34, Nr. 3, 11.2011, S. 507-523.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A n
AU - Holm, Thorsten
AU - Jørgensen, Peter
AU - Rubey, Martin
N1 - Funding Information: This work has been carried out in the framework of the research priority programme SPP 1388 Darstellungstheorie of the Deutsche Forschungsgemeinschaft (DFG). We gratefully acknowledge financial support through the grant HO 1880/4-1.
PY - 2011/11
Y1 - 2011/11
N2 - We give a complete classification of torsion pairs in the cluster category of Dynkin type A n . Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng ( 1005.4364v1 [math.RT, 2010). This allows us to count the number of torsion pairs in the cluster category of type A n . We also count torsion pairs up to Auslander-Reiten translation.
AB - We give a complete classification of torsion pairs in the cluster category of Dynkin type A n . Along the way we give a new combinatorial description of Ptolemy diagrams, an infinite version of which was introduced by Ng ( 1005.4364v1 [math.RT, 2010). This allows us to count the number of torsion pairs in the cluster category of type A n . We also count torsion pairs up to Auslander-Reiten translation.
KW - Clique
KW - Cluster algebra
KW - Cluster tilting object
KW - Generating function
KW - Recursively defined set
KW - Species
KW - Triangulated category
UR - http://www.scopus.com/inward/record.url?scp=80052966428&partnerID=8YFLogxK
U2 - 10.1007/s10801-011-0280-x
DO - 10.1007/s10801-011-0280-x
M3 - Article
AN - SCOPUS:80052966428
VL - 34
SP - 507
EP - 523
JO - Journal of algebraic combinatorics
JF - Journal of algebraic combinatorics
SN - 0925-9899
IS - 3
ER -