On a common generalization of Koszul duality and tilting equivalence

Dag Madsen

Published 2010-07-19Version 1

We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. We give an application to algebras arising from multiplicity free blocks of the BGG category $\mathcal O$.