@article{Koszul Duality for Multigraded Algebras_2012, place={Maryland, USA}, volume={5}, url={https://www.ejpam.com/index.php/ejpam/article/view/1224}, abstractNote={Classical Koszul duality sets up an adjoint pair of functors,Â establishing an equivalence $Â F: D^b(A) \leftrightarrowsÂ D^b(A^!):G,$ where $A$ is a quadratic algebra, $A^!$ is theÂ quadratic dual, and $D^b$ refers to the bounded derived categoryÂ of complexes of graded modules over the graded algebra (i.e., $A$Â or $A^!$). This duality can be extended in many ways. We considerÂ here two extensions: first we wish to allow a $\Lambda$-gradedÂ algebra, where $\Lambda$ is any abelian group (not just $\Z$).Â Second, we will allow filtered algebras. In fact we areÂ considering filtered quadratic algebras with an (internal)Â $\Lambda$-grading.}, number={4}, journal={European Journal of Pure and Applied Mathematics}, year={2012}, month={Nov.}, pages={511–539} }