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Cotorsion pairs in cluster categories of type A^\infty_\infty

Huimin Chang Department of Applied Mathematics, School of Education, The Open University of China, 100039 Beijing, China Yu Zhou Yau Mathematical Sciences Center, Tsinghua University, 100084 Beijing, China Bin Zhu Department of Mathematical Sciences, Tsinghua University, 100084 Beijing, China

Combinatorics Representation Theory mathscidoc:2204.06001

Journal of Combinatorial Theory, Series A, 156, 119-141, 2018.5
In this paper, we give a complete classification of cotorsion pairs in a cluster category C of type A^\infty_\infty via certain configurations of arcs, called τ-compact Ptolemy diagrams, in an infinite strip with marked points. As applications, we classify t-structures and functorially finite rigid subcategories in C, respectively. We also deduce Liu-Paquette's classification of cluster tilting subcategories of C and Ng's classification of torsion pairs in the cluster category of type A^\infty_\infty.
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@inproceedings{huimin2018cotorsion,
  title={Cotorsion pairs in cluster categories of type A^\infty_\infty},
  author={Huimin Chang, Yu Zhou, and Bin Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429164329030432175},
  booktitle={Journal of Combinatorial Theory, Series A},
  volume={156},
  pages={119-141},
  year={2018},
}
Huimin Chang, Yu Zhou, and Bin Zhu. Cotorsion pairs in cluster categories of type A^\infty_\infty. 2018. Vol. 156. In Journal of Combinatorial Theory, Series A. pp.119-141. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429164329030432175.
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