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Decorated Marked Surfaces III: The Derived Category of a Decorated Marked Surface

Aslak Bakke Buan Institutt for matematiske fag , NTNU, N-7491 Trondheim, Norway Yu Qiu Yau Mathematical Sciences Center , Tsinghua University, 100084 Beijing, China Yu Zhou Yau Mathematical Sciences Center , Tsinghua University, 100084 Beijing, China

Representation Theory Rings and Algebras mathscidoc:2204.30001

International Mathematics Research Notices, 2021, (17), 12967-12992, 2021.9
We study the Ginzburg dg algebra Γ_T associated with the quiver with potential arising from a triangulation T of a decorated marked surface S_△⁠, in the sense of [22]. We show that there is a canonical way to identify all finite-dimensional derived categories D_{fd}(Γ_T)⁠, denoted by D_{fd}(S_△)⁠. As an application, we show that the spherical twist group ST(S_△) associated with D_{fd}(S_△) acts faithfully on its space of stability conditions.
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@inproceedings{aslak2021decorated,
  title={Decorated Marked Surfaces III: The Derived Category of a Decorated Marked Surface},
  author={Aslak Bakke Buan, Yu Qiu, and Yu Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429162007714394172},
  booktitle={International Mathematics Research Notices},
  volume={2021},
  number={17},
  pages={12967-12992},
  year={2021},
}
Aslak Bakke Buan, Yu Qiu, and Yu Zhou. Decorated Marked Surfaces III: The Derived Category of a Decorated Marked Surface. 2021. Vol. 2021. In International Mathematics Research Notices. pp.12967-12992. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429162007714394172.
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