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Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization

Yu Zhou Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China Bin Zhu Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China

Combinatorics Representation Theory Rings and Algebras mathscidoc:2204.06002

Algebra and Representation Theory, 21, 817-832, 2017.10
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.
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@inproceedings{yu2017mutation,
  title={Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization},
  author={Yu Zhou, and Bin Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429164618957760176},
  booktitle={Algebra and Representation Theory},
  volume={21},
  pages={817-832},
  year={2017},
}
Yu Zhou, and Bin Zhu. Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization. 2017. Vol. 21. In Algebra and Representation Theory. pp.817-832. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429164618957760176.
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