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A simple proof of Kostant's theorem that U(g) is free over its center
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 118, Number 5, October 1996
- pp. 979-987
- 10.1353/ajm.1996.0037
- Article
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In this paper we present a simple proof of the fundamental result by B. Kostant which claims that the universal enveloping algebra of a reductive Lie algebra g is free over its center. We also indicate how this result allows to simplify the proof of another important result of B. Kostant—the description of the algebra of functions on the nilpotent cone. We use this technique to prove some generalizations of Kostant's theorem. We also deduce from it a way to check which subalgebras of g are "centrally free."