Projective-injective modules, Serre functors and symmetric algebras
Projective-injective modules, Serre functors and symmetric algebras
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DOI：
10.1515/crelle.2008.020
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发表时间：
2005-08
期刊：
影响因子：
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通讯作者：
V. Mazorchuk;C. Stroppel
中科院分区：
文献类型：
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作者：
V. Mazorchuk;C. Stroppel
摘要：我们描述了与半简单复李代数相关的范畴（推广）的Serre函子。在我们的方法中，投影-内射模，即同时是投影和内射的模，起着重要的作用。对于一个自同态环为对称代数的投射内射模，它们控制了具有双中心的拟遗传代数的Serre函子。作为双中心器性质的一个应用，结合我们对Serre函子的描述，证明了Khovanov关于抛物类中投射内射模的三个猜想。
Abstract We describe Serre functors for (generalisations of) the category 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 .