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A characterization of hereditary algebras via thick subcategories


Author: Yuta Kimura
Journal: Proc. Amer. Math. Soc. 148 (2020), 2819-2822
MSC (2010): Primary 16E60, 16E35
DOI: https://doi.org/10.1090/proc/15036
Published electronically: April 9, 2020
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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.


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Additional Information

Yuta Kimura
Affiliation: Fakultät für Mathematik, Universität Bielefeld, 33501 Bielefeld, Germany
Email: ykimura@math.uni-bielefeld.de

DOI: https://doi.org/10.1090/proc/15036
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
Article copyright: © Copyright 2020 American Mathematical Society