Projective-injective modules, Serre functors and symmetric algebras
表示论
2007-06-13 v2
摘要
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.
引用
@article{arxiv.math/0508119,
title = {Projective-injective modules, Serre functors and symmetric algebras},
author = {Volodymyr Mazorchuk and Catharina Stroppel},
journal= {arXiv preprint arXiv:math/0508119},
year = {2007}
}