A characterization of hereditary algebras via thick subcategories
HTML articles powered by AMS MathViewer
- by Yuta Kimura PDF
- Proc. Amer. Math. Soc. 148 (2020), 2819-2822 Request permission
Abstract:
Let $\Lambda$ be a finite dimensional algebra. There exists a natural injective map from the set of wide subcategories in the category of finitely generated $\Lambda$-modules to the set of thick subcategories in the bounded derived category of $\Lambda$.We show, when $\Lambda$ is elementary, that the natural map is bijective if and only if $\Lambda$ is hereditary.References
- Takuma Aihara and Osamu Iyama, Silting mutation in triangulated categories, J. Lond. Math. Soc. (2) 85 (2012), no. 3, 633–668. MR 2927802, DOI 10.1112/jlms/jdr055
- Kristian Brüning, Thick subcategories of the derived category of a hereditary algebra, Homology Homotopy Appl. 9 (2007), no. 2, 165–176. MR 2366948, DOI 10.4310/HHA.2007.v9.n2.a7
- Dieter Happel, Triangulated categories in the representation theory of finite-dimensional algebras, London Mathematical Society Lecture Note Series, vol. 119, Cambridge University Press, Cambridge, 1988. MR 935124, DOI 10.1017/CBO9780511629228
- Kiyoshi Igusa, Shiping Liu, and Charles Paquette, A proof of the strong no loop conjecture, Adv. Math. 228 (2011), no. 5, 2731–2742. MR 2838056, DOI 10.1016/j.aim.2011.06.042
- Henning Krause and Jan Šťovíček, The telescope conjecture for hereditary rings via Ext-orthogonal pairs, Adv. Math. 225 (2010), no. 5, 2341–2364. MR 2680168, DOI 10.1016/j.aim.2010.04.027
- Chao Zhang and Hongyan Cai, A note on thick subcategories and wide subcategories, Homology Homotopy Appl. 19 (2017), no. 2, 131–139. MR 3714363, DOI 10.4310/HHA.2017.v19.n2.a8
Additional Information
- Yuta Kimura
- Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
- MR Author ID: 1121812
- Email: ykimura@math.uni-bielefeld.de
- Received by editor(s): July 2, 2019
- Received by editor(s) in revised form: November 4, 2019
- Published electronically: April 9, 2020
- Additional Notes: The author was supported by the Alexander von Humboldt Stiftung/Foundation in the framework of the Alexander von Humboldt Professorship endowed by the Federal Ministry of Education and Research.
- Communicated by: Jerzy Weyman
- © Copyright 2020 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 2819-2822
- MSC (2010): Primary 16E60, 16E35
- DOI: https://doi.org/10.1090/proc/15036
- MathSciNet review: 4099771