Torsion pairs in cluster tubes

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 obtain that the torsion pairs in cluster tubes exhibit a cyclic sieving phenomenon.

19 pages

References in corpus (6)

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• Weight structures vs. $t$-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)
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Cited by in corpus (4)

• Cotorsion pairs in cluster categories of type $A_{\infty }^{\infty }$
• Classification of cosilting modules in type $\tilde{A}$
• On rooted cluster morphisms and cluster structures in $2$-Calabi-Yau triangulated categories
• Cotorsion pairs and t-structures in a $2-$Calabi-Yau triangulated category