Ptolemy diagrams and cotorsion pairs in m-cluster categories of type A

Abstract

In this paper, we give a complete classification of cotorsion pairs in [Formula: see text]-cluster categories of type [Formula: see text], denoted by [Formula: see text], via certain configurations of [Formula: see text]-diagonals, called Ptolemy diagrams. As applications, we classify [Formula: see text]-rigid subcategories of [Formula: see text], which gives Jacquet–Malo’s classification of [Formula: see text]-cluster tilting subcategories of [Formula: see text]. When [Formula: see text], this generalizes the work of Holm et al. [Ptolemy diagrams and torsion pairs in the cluster category of Dynkin type [Formula: see text], J. Algebraic Combin. 34(3) (2011) 507–523] for the classification of torsion pairs in cluster categories of type [Formula: see text].