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Classification of abelian hereditary directed categories satisfying Serre duality
Author(s):
Adam-Christiaan
van Roosmalen
Journal:
Trans. Amer. Math. Soc.
360
(2008),
2467-2503.
MSC (2000):
Primary 16G20, 16G70, 18E10, 18E30
Posted:
October 30, 2007
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Abstract:
In an ongoing project to classify all hereditary abelian categories, we provide a classification of  -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:
10.1090/S0002-9947-07-04426-1
PII:
S 0002-9947(07)04426-1
Received by editor(s):
February 9, 2006
Posted:
October 30, 2007
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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