Maximal subalgebra associated with a first integral of a system possessing sl(3,R) algebra

Abstract

Conventionally the symmetries of a dynamical system are used to determine the first integrals associated with the system. In this paper the reverse procedure is adopted for one-dimensional systems possessing SL(3,R) symmetry. The equivalence of such systems enables the free particle equation to be used as a vehicle. It is observed that for three particular first integrals, each gives rise to a triplet of generators having isomorphic algebras. It is then shown how the knowledge of a first integral and its associated triplet enables one to obtain the remaining integrals and triplets.