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.
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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.
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Holm, T., Jørgensen, P. & Rubey, M. Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type A n . J Algebr Comb 34, 507–523 (2011). https://doi.org/10.1007/s10801-011-0280-x
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DOI: https://doi.org/10.1007/s10801-011-0280-x