Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules

Abstract

We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak{g}={\mathfrak{gl}}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all $\mathfrak{g}$-modules. This is used to estimate and in some cases determine the global dimension of blocks of the categories of Gelfand-Zeitlin and Whittaker modules.

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Cited by in corpus (6)

• Whittaker modules for classical Lie superalgebras
• Category O for Takiff sl_2
• Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras
• Homological epimorphisms, recollements and Hochschild cohomology - with a conjecture by Snashall-Solberg in view
• Some homological properties of category O. III
• Annihilator ideals and blocks of Whittaker modules over quasireductive Lie superalgebras