TY - JOUR
T1 - Hereditary uniserial categories with serre duality
AU - Van Roosmalen, Adam Christiaan
N1 - Funding Information:
Acknowledgements The author wishes to thank Michel Van den Bergh for meaningful discussions, and wishes to thank Jan Št’ovícˇek and Joost Vercruysse for many useful comments on an early draft. The author gratefully acknowledges the support of the Hausdorff Center for Mathematics in Bonn, and the Collaborative Research Center 701 during his visit to Bielefeld University.
PY - 2012/12
Y1 - 2012/12
N2 - An abelian Krull-Schmidt category is said to be uniserial if the isomorphism classes of subobjects of a given indecomposable object form a linearly ordered poset. In this paper, we classify the hereditary uniserial categories with Serre duality. They fall into two types: the first type is given by the representations of the quiver An with linear orientation (and infinite variants thereof), the second type by tubes (and an infinite variant). These last categories give a new class of hereditary categories with Serre duality, called big tubes.
AB - An abelian Krull-Schmidt category is said to be uniserial if the isomorphism classes of subobjects of a given indecomposable object form a linearly ordered poset. In this paper, we classify the hereditary uniserial categories with Serre duality. They fall into two types: the first type is given by the representations of the quiver An with linear orientation (and infinite variants thereof), the second type by tubes (and an infinite variant). These last categories give a new class of hereditary categories with Serre duality, called big tubes.
KW - Hereditary categories
KW - Serre duality
UR - http://www.scopus.com/inward/record.url?scp=84894539422&partnerID=8YFLogxK
U2 - 10.1007/s10468-011-9289-z
DO - 10.1007/s10468-011-9289-z
M3 - Article
AN - SCOPUS:84894539422
SN - 1386-923X
VL - 15
SP - 1291
EP - 1322
JO - Algebras and Representation Theory
JF - Algebras and Representation Theory
IS - 6
ER -