Geodesic
Quasidifferential operator and quantum argument shift method
Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 1, pp. 33-39

Voir la notice de l'article provenant de la source Math-Net.Ru

We describe an explicit formula for the first-order quasiderivation of an arbitrary central element of the universal enveloping algebra of a general linear Lie algebra. We apply it to show that derivations of any two central elements of the universal enveloping algebra commute. This contributes to the Vinberg problem of finding commutative subalgebras in universal enveloping algebras with the underlying Poisson algebras determined by the argument shift method.
Keywords: universal enveloping algebra, Lie algebra, quantum argument shift method
Mots-clés : deformation quantization. 
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     author = {Y. Ikeda},
     title = {Quasidifferential operator and quantum argument shift method},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2022_212_1_a2/}
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Y. Ikeda. Quasidifferential operator and quantum argument shift method. Teoretičeskaâ i matematičeskaâ fizika, Tome 212 (2022) no. 1, pp. 33-39. http://geodesic.mathdoc.fr/item/TMF_2022_212_1_a2/