THE LIE ALGEBRA sl(3, R) AND LINEARIZATION

Abstract

Abstract In a previous paper (see [10]) we established the form of second-order ordinary differential equations with two commuting symmetries (in canonical form G1 = ∂/∂, G2 = ∂/∂q, G2 ≠ p(q,t)G1) which have the Lie algebra sl(3, R). In this paper we determine the conditions under which an equation with two non-commuting (non-proportional) symmetries possesses the Lie algebra sl(3, R). We also obtain the most general nonlinear equation at most linear in the first derivative which has sl(3, R) algebra. AMS Subject Classification: 34A3422E70