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Three-dimensional Lie algebras of transformations of the plane. (English. Russian original) Zbl 0527.51028

Sib. Math. J. 23, 694-702 (1983); translation from Sib. Mat. Zh. 23, No. 5, 132-141 (1982).

MSC:

51N25 Analytic geometry with other transformation groups
17B05 Structure theory for Lie algebras and superalgebras
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
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References:

[1] H. Poincaré, ?Sur les hypothèses fondamentales de la géometrie,? Bull. Soc. Math. France,15, 203-216 (1887); Oeuvres de H. Poincaré, Vols. I?XI, Gauthier-Villars, Paris (1916-1956). · JFM 19.0512.01
[2] A. Z. Petrov, New Methods in the General Theory of Relativity [in Russian], Nauka, Moscow (1966). · Zbl 0203.19602
[3] S. Lie and F. Engel, Teorie der Transformationsgruppen, Vol. 3, Teubner, Leipzig (1893).
[4] N. G. Chebotarev, Theorie of Lie Groups [in Russian], Gostekhizdat, Moscow (1940).
[5] L. V. Ovsyannikov, Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978). · Zbl 0484.58001
[6] L. P. Eisenhart, Continuous Groups of Transformations, Dover, New York (1961). · Zbl 0096.02103
[7] I. M. Yaglom, The Galilean Relativity Principle and Non-Euclidean Geometry [in Russian], Nauka, Moscow (1969). · Zbl 0202.52901
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