From triangulated categories to module categories via localisation
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- by Aslak Bakke Buan and Bethany R. Marsh PDF
- Trans. Amer. Math. Soc. 365 (2013), 2845-2861
Abstract:
We show that the category of finite dimensional modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category is equivalent to the Gabriel-Zisman localisation of the category with respect to a certain class of maps. This generalises the $2$-Calabi-Yau tilting theorem of Keller-Reiten, in which the module category is obtained as a factor category, to the rigid case.References
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Additional Information
- Aslak Bakke Buan
- Affiliation: Institutt for matematiske fag, Norges teknisk-naturvitenskapelige universitet, N-7491 Trondheim, Norway
- Email: aslakb@math.ntnu.no
- Bethany R. Marsh
- Affiliation: School of Mathematics, University of Leeds, Leeds, LS2 9JT, United Kingdom
- MR Author ID: 614298
- ORCID: 0000-0002-4268-8937
- Received by editor(s): November 17, 2010
- Received by editor(s) in revised form: March 1, 2011
- Published electronically: November 7, 2012
- Additional Notes: This work was supported by the Engineering and Physical Sciences Research Council [grant number EP/G007497/1] and by the NFR [FRINAT grant number 196600].
- © Copyright 2012 Aslak Bakke Buan and Bethany R. Marsh
- Journal: Trans. Amer. Math. Soc. 365 (2013), 2845-2861
- MSC (2010): Primary 18E30, 18E35, 16G20; Secondary 13F60
- DOI: https://doi.org/10.1090/S0002-9947-2012-05631-5
- MathSciNet review: 3034450