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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Classification of abelian hereditary directed categories satisfying Serre duality
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by Adam-Christiaan van Roosmalen PDF
Trans. Amer. Math. Soc. 360 (2008), 2467-2503 Request permission

Abstract:

In an ongoing project to classify all hereditary abelian categories, we provide a classification of $\operatorname {Ext}$-finite directed hereditary abelian categories satisfying Serre duality up to derived equivalence. In order to prove the classification, we will study the shapes of Auslander-Reiten components extensively and use appropriate generalizations of tilting objects and coordinates, namely partial tilting sets and probing of objects by quasi-simples.
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Additional Information
  • Adam-Christiaan van Roosmalen
  • Affiliation: Research Group Algebra, Hasselt University, Agoralaan, gebouw D, B-3590 Diepenbeek, Belgium
  • Email: AdamChristiaan.vanRoosmalen@UHasselt.be
  • Received by editor(s): February 9, 2006
  • Published electronically: October 30, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 2467-2503
  • MSC (2000): Primary 16G20, 16G70, 18E10, 18E30
  • DOI: https://doi.org/10.1090/S0002-9947-07-04426-1
  • MathSciNet review: 2373322