Details
| Original language | English |
|---|---|
| Pages (from-to) | 587-605 |
| Number of pages | 19 |
| Journal | Journal of algebraic combinatorics |
| Volume | 39 |
| Issue number | 3 |
| Publication status | Published - May 2014 |
Abstract
We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on torsion pairs in cluster categories of Dynkin type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in cluster tubes, and find that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon.
Keywords
- Auslander-Reiten quiver, Cluster category, Cluster tilting object, Triangulated category, Tube
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Journal of algebraic combinatorics, Vol. 39, No. 3, 05.2014, p. 587-605.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Torsion pairs in cluster tubes
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 grants HO 1880/4-1 and HO 1880/5-1.
PY - 2014/5
Y1 - 2014/5
N2 - We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on torsion pairs in cluster categories of Dynkin type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in cluster tubes, and find that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon.
AB - We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on torsion pairs in cluster categories of Dynkin type A. As a consequence of our classification we establish closed formulae enumerating the torsion pairs in cluster tubes, and find that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon.
KW - Auslander-Reiten quiver
KW - Cluster category
KW - Cluster tilting object
KW - Triangulated category
KW - Tube
UR - http://www.scopus.com/inward/record.url?scp=84897577183&partnerID=8YFLogxK
U2 - 10.1007/s10801-013-0457-6
DO - 10.1007/s10801-013-0457-6
M3 - Article
AN - SCOPUS:84897577183
VL - 39
SP - 587
EP - 605
JO - Journal of algebraic combinatorics
JF - Journal of algebraic combinatorics
SN - 0925-9899
IS - 3
ER -