Geodesic
On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$
Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1375-1382 
A. A. Tarasov. On some commutative subalgebras of the universal enveloping algebra of the Lie algebra $\mathfrak{gl}(n,\mathbb C)$. Sbornik. Mathematics, Tome 191 (2000) no. 9, pp. 1375-1382. http://geodesic.mathdoc.fr/item/SM_2000_191_9_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

For the Lie algebra $\mathfrak g=\mathfrak{gl}(n,\mathbb C)$ it is proved that the maximal commutative subalgebras of the Poisson algebra $P(\mathfrak g)$ obtained by the method of shifting the invariants can be lifted to the enveloping algebra. Moreover, this lifting can be carried out by means of the symmetrization map.

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