A simple proof of Kostant's theorem that U(g) is free over its center

Joseph Bernstein*, Valery Lunts

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.".

Original languageEnglish
Pages (from-to)979-987
Number of pages9
JournalAmerican Journal of Mathematics
Volume118
Issue number5
DOIs
StatePublished - Oct 1996

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