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 -