Some homological properties of category O. III

Abstract

We prove that thick category $\mathcal{O}$ associated to a semi-simple complex finite dimensional Lie algebra is extension full in the category of all modules. We also prove the weak Alexandru conjecture both for regular blocks of thick category $\mathcal{O}$ and the associated categories of Harish-Chandra bimodules, but disprove it for singular blocks.

References in corpus (7)

• Koszul duality of translation--and Zuckerman functors
• Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology
• Transitive 2-representations of finitary 2-categories
• Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules
• Homological invariants in category O for the general linear superalgebra
• Dualities and derived equivalences for category O
• Bott-Borel-Weil theory, BGG reciprocity and twisting functors for Lie superalgebras

Cited by in corpus (5)

• Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules
• Some homological properties of category $\mathcal{O}$, V
• Homological epimorphisms, recollements and Hochschild cohomology - with a conjecture by Snashall-Solberg in view
• Dualities and derived equivalences for category O
• Dirac cohomology and Euler-Poincaré pairing for weight modules