Abstract
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, Poincare, Lobachevskii, de Sitter, Carroll, and other spaces.
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