TY - JOUR
TI - Koszul Duality for Multigraded Algebras
PY - 2012/11/07
Y2 - 2024/06/17
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 5
IS - 4
LA - en
UR - https://www.ejpam.com/index.php/ejpam/article/view/1224
SP - 511-539
AB - 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.
ER -