Torsion pairs in cluster tubes

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  • Newcastle University
  • TU Wien (TUW)
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Original languageEnglish
Pages (from-to)587-605
Number of pages19
JournalJournal of algebraic combinatorics
Volume39
Issue number3
Publication statusPublished - 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

Cite this

Torsion pairs in cluster tubes. / Holm, Thorsten; Jørgensen, Peter; Rubey, Martin.
In: Journal of algebraic combinatorics, Vol. 39, No. 3, 05.2014, p. 587-605.

Research output: Contribution to journalArticleResearchpeer review

Holm T, Jørgensen P, Rubey M. Torsion pairs in cluster tubes. Journal of algebraic combinatorics. 2014 May;39(3):587-605. doi: 10.1007/s10801-013-0457-6
Holm, Thorsten ; Jørgensen, Peter ; Rubey, Martin. / Torsion pairs in cluster tubes. In: Journal of algebraic combinatorics. 2014 ; Vol. 39, No. 3. pp. 587-605.
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