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KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

Published online by Cambridge University Press:  21 September 2010

VOLODYMYR MAZORCHUK*
Affiliation:
Department of Mathematics, Uppsala University, SE 471 06, Uppsala, Sweden (email: mazor@math.uu.se)
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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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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