Mutation of torsion pairs in triangulated categories and its geometric realization

Abstract

We introduce and study mutation of torsion pairs, as a generalization of mutation of cluster tilting objects, rigid objects and maximal rigid objects. It is proved that any mutation of a torsion pair is again a torsion pair. A geometric realization of mutation of torsion pairs in the cluster category of type $A_n$ or $A_{\infty }$ is given via rotation of Ptolemy diagrams.

Updated version

References in corpus (6)

• On triangulated orbit categories
• Coloured quivers for rigid objects and partial triangulations: The unpunctured case
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• On a triangulated category which behaves like a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon
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Cited by in corpus (4)

• Cluster tilting vs. weak cluster tilting in Dynkin type A infinity
• Cluster subalgebras and cotorsion pairs in Frobenius extriangulated categories
• Torsion pairs in finite $2$-Calabi-Yau triangulated categories with maximal rigid objects
• Triangulated quotient categories