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A primitive ideal of \({\mathcal U(G}[X])\) contracting to a primitive ideal of \({\mathcal U(G)}\). (Un idéal primitif de \({\mathcal U(G}[X])\) se contracte en un idéal primitif de \({\mathcal U(G)}\).) (French) Zbl 0847.17008
Let \({\mathfrak g}\) be a finite-dimensional Lie algebra over a field of characteristic zero and \(U:= U({\mathfrak g})\) its enveloping algebra. This paper gives an elementary proof that a primitive ideal of \(U[ x]\), the polynomial ring in one variable over \(U\), contracts to a primitive ideal of \(U\). This may be regarded as a slight strengthening of the well-known fact that \(U\) is Jacobson.
MSC:
17B35 Universal enveloping (super)algebras
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