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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Classification of abelian hereditary directed categories satisfying Serre duality


Author: Adam-Christiaan van Roosmalen
Journal: Trans. Amer. Math. Soc. 360 (2008), 2467-2503
MSC (2000): Primary 16G20, 16G70, 18E10, 18E30
Published electronically: October 30, 2007
MathSciNet review: 2373322
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-07-04426-1
PII: S 0002-9947(07)04426-1
Received by editor(s): February 9, 2006
Published electronically: October 30, 2007
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.