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

[摘要] 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.

[关键词] extension fullness;Gelfand–Zeitlin modules;Whittaker modules;Yoneda extensions;homological dimension