TY - JOUR
T1 - Classification of abelian hereditary directed categories satisfying serre duality
AU - Van Roosmalen, ADam Christiaan
PY - 2008/5
Y1 - 2008/5
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=74849083517&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-07-04426-1
DO - 10.1090/S0002-9947-07-04426-1
M3 - Article
AN - SCOPUS:74849083517
SN - 0002-9947
VL - 360
SP - 2467
EP - 2503
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 5
ER -