Connected subgroups of the conformal group C(1, 4)

A method is given for describing maximal subalgebras of rank r, 1 r 4, of the conformal algebra AC(1, 4), which is the maximal invariance algebra of the eikonal equation. With the help of this method a classification is made up to C(1, 4)-equivalence of all maximal subalgebras L of rank 1, 2, 3, and 4 of the algebra AC(1, 4) satisfying the condition L V p₁, P₂, P₃, p₄, where V is the space of translations.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7–8, pp. 870–884, July–August, 1991.