Projective-injective modules, Serre functors and symmetric algebras

By Volodymyr Mazorchuk, C. Stroppel. 2005

85 citations recorded by the source corpus.

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 .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5da37d3f12874e10cda91b49d78686c19a6d0056

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Centers of degenerate cyclotomic Hecke algebras and parabolic category (2006, background): “Proof. As explained in the proof of [ MS , Theorem 5.4], there is an adjoint pair (F,G) of functors (which are compositions of certain derived Zuckerman functors) between the bounded derived categories”
Some homological properties of the category O (2007, methodology): “category LC(T) (see [ MOS , Proposition 11]).”