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Maximal rigid subcategories in 2-Calabi–Yau triangulated categories

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

Representation Theory Rings and Algebras mathscidoc:2204.30004

Journal of Algebra, 348, (1), 49-60, 2011.12
We study the functorially finite maximal rigid subcategories in 2-CY triangulated categories and their endomorphism algebras. Cluster tilting subcategories are obviously functorially finite and maximal rigid; we prove that the converse is true if the 2-CY triangulated categories admit a cluster tilting subcategory. As a generalization of a result of Keller and Reiten (2007) [KR], we prove that any functorially finite maximal rigid subcategory is Gorenstein with Gorenstein dimension at most 1. Similar as cluster tilting subcategory, one can mutate maximal rigid subcategories at any indecomposable object. If two maximal rigid objects are reachable via simple mutations, then their endomorphism algebras have the same representation type.
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@inproceedings{yu2011maximal,
  title={Maximal rigid subcategories in 2-Calabi–Yau triangulated categories},
  author={Yu Zhou, and Bin Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429170906207624181},
  booktitle={Journal of Algebra},
  volume={348},
  number={1},
  pages={49-60},
  year={2011},
}
Yu Zhou, and Bin Zhu. Maximal rigid subcategories in 2-Calabi–Yau triangulated categories. 2011. Vol. 348. In Journal of Algebra. pp.49-60. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429170906207624181.
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