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Projective-injective modules, Serre functors and symmetric algebras

Volodymyr Mazorchuk·Catharina Stroppel
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Abstract

We describe Serre functors for (generalisations of) the category O associated with a semi-simple complex Lie algebra. In our approach, projective-injective modules play an important role. They control the Serre functor in the case of a quasi-hereditary algebra having a double centraliser property with respect to a symmetric algebra. As an application of the double centraliser property and our description of Serre functors, we prove three conjectures of Khovanov about the projective-injective modules in the parabolic category O for sl_n.

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Volodymyr Mazorchuk, Catharina Stroppel. 2005-09-06. Projective-injective modules, Serre functors and symmetric algebras. https://arxiv.org/abs/math/0508119

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