RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (1170 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{Gro81} \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 \mathnet{http://mi.mathnet.ru/tmf2467} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=661607} \zmath{https://zbmath.org/?q=an:0494.53046} \transl \jour Theoret. and Math. Phys. \yr 1981 \vol 49 \issue 2 \pages 987--993 \crossref{https://doi.org/10.1007/BF01028993} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981NV49900007}