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Krull dimension of the enveloping algebra of a semisimple Lie algebra


Author: Thierry Levasseur
Journal: Proc. Amer. Math. Soc. 130 (2002), 3519-3523
MSC (2000): Primary 16Sxx, 17Bxx
Published electronically: May 15, 2002
MathSciNet review: 1918828
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Abstract: Let $\mathfrak{g}$ be a complex semisimple Lie algebra and $U(\mathfrak{g})$ be its enveloping algebra. We deduce from the work of R. Bezrukavnikov, A. Braverman and L. Positselskii that the Krull-Gabriel-Rentschler dimension of $U(\mathfrak{g})$ is equal to the dimension of a Borel subalgebra of $\mathfrak{g}$.


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Additional Information

Thierry Levasseur
Affiliation: Département de Mathématiques, Université de Brest, 29285 Brest cedex, France
Email: Thierry.Levasseur@univ-brest.fr

DOI: https://doi.org/10.1090/S0002-9939-02-06507-3
Keywords: Krull dimension, semisimple Lie algebra, enveloping algebra, differential operators
Received by editor(s): July 30, 2001
Published electronically: May 15, 2002
Communicated by: Lance W. Small
Article copyright: © Copyright 2002 American Mathematical Society