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This article is cited in 7 scientific papers (total in 7 papers)
Extension Fullness of the Categories of Gelfand–Zeitlin and Whittaker Modules
Kevin Coulembiera, Volodymyr Mazorchukb a Department of Mathematical Analysis, Ghent University, Krijgslaan 281, 9000 Gent, Belgium
b Department of Mathematics, Uppsala University, Box 480, SE-751 06, Uppsala, Sweden
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.
Keywords:
extension fullness; Gelfand–Zeitlin modules; Whittaker modules; Yoneda extensions; homological dimension.
Received: September 25, 2014; in final form February 20, 2015; Published online February 24, 2015
Citation:
Kevin Coulembier, Volodymyr Mazorchuk, “Extension Fullness of the Categories of Gelfand–Zeitlin and Whittaker Modules”, SIGMA, 11 (2015), 016, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma997 https://www.mathnet.ru/eng/sigma/v11/p16
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Abstract page: | 242 | Full-text PDF : | 43 | References: | 39 |
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