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

2023/12/05 by Huimin Chang, Chang, Huimin
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2312.02526

openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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