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Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization

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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.

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Acknowledgements

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

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Author notes

  1. Yu Zhou

    Present address: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491, Trondheim, Norway

Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, 100084, Beijing, China

    Yu Zhou & Bin Zhu

Authors
  1. Yu Zhou
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  2. Bin Zhu
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Corresponding author

Correspondence to Yu Zhou.

Additional information

Presented by Steffen Koenig.

The authors are supported by the NSF of China (Grants 11671221). The first author is also supported by FRINAT grant number 231000, from the Norwegian Research Council.

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Zhou, Y., Zhu, B. Mutation of Torsion Pairs in Triangulated Categories and its Geometric Realization. Algebr Represent Theor 21, 817–832 (2018). https://doi.org/10.1007/s10468-017-9740-x

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  • DOI: https://doi.org/10.1007/s10468-017-9740-x

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