Kalnins, Ernie G.Miller, W., Jr.2008-11-032008-11-031977-02Kalnins, E.G. & Miller, W., Jr. (1977). Lie theory and the wave equation in space–time. 3. Semisubgroup coordinates. Journal of Mathematical Physics, 18, 271.0022-2488https://hdl.handle.net/10289/1235We classify and study those coordinate systems which permit R separation of variables for the wave equation in four-dimensional space–time and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss over 100 such systems and relate them to orbits of triplets of commuting operators in the enveloping algebra of the conformal group SO(4,2).application/pdfenCopyright 1977 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspMathematicsJournal Article10.1063/1.523246