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KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

Part of: Representation theory of rings and algebras Rings and algebras arising under various constructions

Published online by Cambridge University Press:  21 September 2010

VOLODYMYR MAZORCHUK
VOLODYMYR MAZORCHUK*
Affiliation:
Department of Mathematics, Uppsala University, SE 471 06, Uppsala, Sweden (email: [email protected])
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Abstract

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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.

Keywords

stratified algebraKoszul algebratilting moduleRingel duality

MSC classification

Secondary: 16S37: Quadratic and Koszul algebras 16G10: Representations of Artinian rings
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 1 , August 2010 , pp. 23 - 49
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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