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- W2952585816 abstract "The paper studies quadratic and duality for modules over positively graded categories. Typical examples are modules over a path algebra, which is graded by the path length, of a not necessarily finite quiver with relations. We present a very general definition of quadratic and duality functors backed up by explicit examples. This generalises previous results in two substantial ways: We work in the setup of graded categories, i.e. we allow infinitely many idempotents and also define a ``Koszul'' duality functor for not necessarily categories. As an illustration of the techniques we reprove the duality of translation and Zuckerman functors for the classical category O in a quite elementary and explicit way. As applications we propose a definition of a Koszul dual category for integral blocks of Harish-Chandra bimodules and for blocks outside the critical hyperplanes for the Kac-Moody category O." @default.
- W2952585816 created "2019-06-27" @default.
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- W2952585816 date "2006-03-20" @default.
- W2952585816 modified "2023-09-27" @default.
- W2952585816 title "Quadratic duals, Koszul dual functors, and applications" @default.
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