Koszul duality for multigraded algebras

Abstract

Classical Koszul duality sets up an adjoint pair of functors, establishing an equivalence $F : D^b(A) leftrightarrows D^b(A^!) : G$, where A is a quadratic algebra, $A^!$ is the quadratic dual, and $D^b$ refers to the bounded derived category of complexes of graded modules over the graded algebra (i.e., A or $A^!$). This duality can be extended in many ways. We consider here two extensions: first we wish to allow a $Lambda$-graded algebra, where is any abelian group (not just $Bbb{Z}$). Second, we will allow filtered algebras. In fact we are considering filtered quadratic algebras with an (internal) -grading.