Krull dimension of the enveloping algebra of a semisimple Lie algebra

Levasseur, Thierry

doi:10.1090/S0002-9939-02-06507-3

Krull dimension of the enveloping algebra of a semisimple Lie algebra
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Proc. Amer. Math. Soc. 130 (2002), 3519-3523 Request permission

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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