Geodesic
Casimir operators of groups of motions of spaces of constant curvature
Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 2, pp. 210-218 
N. A. Gromov. Casimir operators of groups of motions of spaces of constant curvature. Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 2, pp. 210-218. http://geodesic.mathdoc.fr/item/TMF_1981_49_2_a6/
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     author = {N. A. Gromov},
     title = {Casimir operators of groups of motions of spaces of constant curvature},
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     url = {http://geodesic.mathdoc.fr/item/TMF_1981_49_2_a6/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Limit transitions are constructed between the generators (Casimir operators) of the center of the universal covering algebra for the Lie algebras of the groups of motions of $n$-dimensional spaces of constant curvature. A method is proposed for obtaining the Casimir operators of a group of motions of an arbitrary $n$-dimensional space of constant curvature from the known Casimir operators of the group $SO(n+1)$. The method is illustrated for the example of the groups of motions of four-dimensional spaces of constant curvature, namely, the Galileo, Poincaré, Lobachevskii, de Sitter, Carroll, and other spaces.

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