Mikhaĭlichenko, G. G. 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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page 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 Keywords:Lobachevskij plane; Galilean plane; anti-pseudo-Euclidean plane; three- dimensional Lie algebras of transformations of the plane; Lie group of local transformations of the plane; groups of motions PDFBibTeX XMLCite \textit{G. G. Mikhaĭlichenko}, Sib. Math. J. 23, 694--702 (1982; Zbl 0527.51028); translation from Sib. Mat. Zh. 23, No. 5, 132--141 (1982) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.