A silting theorem

Aslak Bakke Buan Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway Yu Zhou Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway

Representation Theory mathscidoc:2204.30002

Journal of Pure and Applied Algebra, 220, (7), 2748-2770, 2016.7
We give a generalization of the classical tilting theorem of Brenner and Butler. We show that for a 2-term silting complex P in the bounded homotopy category K^b(proj A) of finitely generated projective modules of a finite dimensional algebra A, the algebra B=End_{K^b(proj A)}(P) admits a 2-term silting complex Q with the following properties: (i) The endomorphism algebra of Q in K^b(proj B) is a factor algebra of A, and (ii) there are induced torsion pairs in mod A and mod B, such that we obtain natural equivalences induced by Hom- and Ext-functors. Moreover, we show how the Auslander–Reiten theory of mod B can be described in terms of the Auslander–Reiten theory of mod A.
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@inproceedings{aslak2016a,
  title={A silting theorem},
  author={Aslak Bakke Buan, and Yu Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429165910514012178},
  booktitle={Journal of Pure and Applied Algebra},
  volume={220},
  number={7},
  pages={2748-2770},
  year={2016},
}
Aslak Bakke Buan, and Yu Zhou. A silting theorem. 2016. Vol. 220. In Journal of Pure and Applied Algebra. pp.2748-2770. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220429165910514012178.
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