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arXiv · 2312.02526

Ptolemy diagrams and torsion pairs in m-cluster categories of type D

Huimin Chang
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Abstract

In this paper, we give a complete classification of torsion pairs in m-cluster categories of type D when m is odd, denoted by CmDn, via a bijection to combinatorial objects called Ptolemy diagrams of type D. As applications, we classify m-rigid subcategories of CmDn, which gives Jacquet-Malo's classification of m-cluster tilting subcategories of CmDn. When m = 1, we generalizes the work of Holm, Jorgensen and Rubey for the classification of torsion pairs in cluster categories of type Dn.

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Huimin Chang. 2023-12-05. Ptolemy diagrams and torsion pairs in m-cluster categories of type D. https://arxiv.org/abs/2312.02526

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