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Title: | Classification of abelian hereditary directed categories satisfying Serre duality | Authors: | VAN ROOSMALEN, Adam-Christiaan | Issue Date: | 2008 | Publisher: | AMER MATHEMATICAL SOC | Source: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 360(5). p. 2467-2503 | Abstract: | In an ongoing project to classify all hereditary abelian categories, we provide a classification of 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. | Notes: | Hasselt Univ, Res Grp Algebra, B-3590 Diepenbeek, Belgium.Van Roosmalen, AC, Hasselt Univ, Res Grp Algebra, Gebouw D, B-3590 Diepenbeek, Belgium.AdamChristiaan.vanRoosmalen@UHasselt.be | Document URI: | http://hdl.handle.net/1942/8007 | ISSN: | 0002-9947 | e-ISSN: | 1088-6850 | DOI: | 10.1090/S0002-9947-07-04308-5 | ISI #: | 000252879200010 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2009 |
Appears in Collections: | Research publications |
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