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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A characterization of hereditary algebras via thick subcategories
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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.
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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