Abstract

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."

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