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Projective-injective modules, Serre functors and symmetric algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra, Geometry and Logic. (Algebra)
2008 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, Vol. 616, 131-165 p.Article in journal (Refereed) Published
Abstract [en]

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).

Place, publisher, year, edition, pages
2008. Vol. 616, 131-165 p.
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URN: urn:nbn:se:uu:diva-105800DOI: 10.1515/CRELLE.2008.020ISI: 000254393000006OAI: oai:DiVA.org:uu-105800DiVA: diva2:222503
Available from: 2009-06-08 Created: 2009-06-08 Last updated: 2009-11-12Bibliographically approved

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Algebra, Geometry and Logic
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Journal für die Reine und Angewandte Mathematik

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