Mazorchuk, V. and Stroppel, C. (2008) Projective-injective modules, Serre functors and symmetric algebras. Journal für die reine und angewandte Mathematik (Crelles Journal), 2008(616), pp. 131-165. (doi: 10.1515/CRELLE.2008.020)
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Publisher's URL: http://dx.doi.org/10.1515/CRELLE.2008.020
Abstract
We describe Serre functors for (generalisations of) the category O associated with a semisimple complex Lie algebra. In our approach, projective-injective modules, that is modules which are both, projective and injective, play an important role. They control the Serre functor in the case of a quasi-hereditary algebra having a double centraliser with respect to a projective-injective module whose endomorphism ring is a symmetric algebra. As an application of the double centraliser property together with our description of Serre functors, we prove three conjectures of Khovanov about the projective-injective modules in the parabolic category O-0(mu)(SIn).
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Stroppel, Dr Catharina and Mazorchuk, Dr Volodymyr |
| Authors: | Mazorchuk, V., and Stroppel, C. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal für die reine und angewandte Mathematik (Crelles Journal) |
| Publisher: | Walter de Gruyter |
| ISSN: | 1435-5345 |
| ISSN (Online): | 0075-4102 |
| Published Online: | 13 May 2008 |
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