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Differential operators and invariant measures. (Opérateurs différentiels et mesures invariantes.) (French) Zbl 0792.17022
Let \({\mathfrak g}\) be a finite dimensional Lie algebra over a field \(k\) of characteristic zero. In the case when \(\mathfrak g\) is nilpotent J. Dixmier [Lect. Notes. Math. 728, 42-63 (1979; Zbl 0409.22003)]constructed a primitive ideal of the enveloping algebra of \({\mathfrak g}\) associated with an orbit of the coadjoint representation of \({\mathfrak g}\). To this end, J. Dixmier used a lemma on the differential operators with polynomial coefficients. The statement of this lemma was proved under some hypotheses (on \(k\), \({\mathfrak g}\), etc.).
In the present paper the author proves a generalization of this lemma in the case when some of these hypotheses are not satisfied anymore.
Reviewer: V.L.Popov (Moskva)

MSC:
17B99 Lie algebras and Lie superalgebras
17B35 Universal enveloping (super)algebras
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