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Quadratic duals , Koszul dual functors , and applications
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mazorchuk, Volodymyr Ovsienko, S. A. |
| Copyright Year | 2006 |
| Abstract | The paper studies quadratic and Koszul 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 Koszul duality functors backed up by explicit examples. This generalises [BGS] 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 Koszul categories. As an illustration of the techniques we reprove the Koszul duality ([RH]) 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. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.uu.se/~mazor/PREPRINTS/CATEG/mos.pdf |
| Alternate Webpage(s) | http://www2.math.uu.se/~mazor/PREPRINTS/CATEG/mos.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0603475v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0603475v3.pdf |
| Alternate Webpage(s) | http://www.math.uu.se/research/pub/Mazorchuk35.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Backup Categories Dual Fenchel's duality theorem Preparation Quadratic function Quiver |
| Content Type | Text |
| Resource Type | Article |
