KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS
2010 (English)In: Journal of the Australian Mathematical Society, ISSN 1446-7887, E-ISSN 1446-8107, Vol. 89, no 1, 23-49 p.Article in journal (Refereed) Published
We give a complete picture of the interaction between the Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras, imposing the condition that standard filtrations of projective modules are finite, and develop a tilting theory for such algebras. Under the assumption on existence of linear tilting (co)resolutions we show that algebras from this class are Koszul, that both the Ringel and Koszul duals belong to the same class, and that these two dualities on this class commute.
Place, publisher, year, edition, pages
2010. Vol. 89, no 1, 23-49 p.
stratified algebra, Koszul algebra, tilting module, Ringel duality
IdentifiersURN: urn:nbn:se:uu:diva-135334DOI: 10.1017/S1446788710001497ISI: 000283959400004OAI: oai:DiVA.org:uu-135334DiVA: diva2:375530