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TMF, 1981, Volume 49, Number 2, Pages 210–218 (Mi tmf2467)  

Casimir operators of groups of motions of spaces of constant curvature

N. A. Gromov


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, Poincaré, Lobachevskii, de Sitter, Carroll, and other spaces.

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English version:
Theoretical and Mathematical Physics, 1981, 49:2, 987–993

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Received: 01.06.1980

Citation: N. A. Gromov, “Casimir operators of groups of motions of spaces of constant curvature”, TMF, 49:2 (1981), 210–218; Theoret. and Math. Phys., 49:2 (1981), 987–993

Citation in format AMSBIB
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\by N.~A.~Gromov
\paper Casimir operators of groups of motions of spaces of constant curvature
\jour TMF
\yr 1981
\vol 49
\issue 2
\pages 210--218
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=661607}
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\transl
\jour Theoret. and Math. Phys.
\yr 1981
\vol 49
\issue 2
\pages 987--993
\crossref{https://doi.org/10.1007/BF01028993}
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