Quasi-hereditary algebras and generalized Koszul duality

Abstract

We present an easily applicable sufficient condition for standard Koszul algebras to be Koszul with respect to $\Delta$. If a quasi-hereditary algebra \L is Koszul with respect to $\Delta$, then \L and the Yoneda extension algebra of $\Delta$ are Koszul dual in a sense explained below, implying in particular that their bounded derived categories of finitely generated graded modules are equivalent. We also prove that the extension algebra of $\Delta$ is Koszul in the classical sense.Comment: This is a revised and updated version of the last section of arXiv:1007.328