Geodesic
Casimir operators of groups of motions of spaces of constant curvature
Teoretičeskaâ i matematičeskaâ fizika, Tome 49 (1981) no. 2, pp. 210-218

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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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     author = {N. A. Gromov},
     title = {Casimir operators of groups of motions of spaces of constant curvature},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {210--218},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1981_49_2_a6/}
}
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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/