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Algebras and Representation Theory

, Volume 21, Issue 4, pp 817–832 | Cite as

Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization

  • Yu Zhou
  • Bin Zhu
Article

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 is given via rotation of Ptolemy diagrams.

Keywords

Torsion pairs Triangulated categories Mutations Ptolemy diagrams 

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Notes

Acknowledgements

The authors thank the anonymous referee for his/her useful suggestions to improve this article.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway

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