LIOUVILLE EQUATION .5. THE FULL SYMMETRIES OF R(-1)-POTENTIALS

A systematic study of the symmetries of Liouville's equation for r-1-p otential is presented. The canonical transformations in phase space wh ich leave the hamiltonian invariant turn out to be the full symmetry t ransformations of Liouville's operator, as well. The symmetry group is SO(4). A maximal set of mutually commuting operators, and subsequentl y, a classification of the eigensolutions of Liouville operator is pro posed. The Kustaanheimo-Stiefel transformation is used to show that th is SO(4) is isomorphic to a constrained SU(4) and contains all symmetr ies of Liouville's equation for r-1-potential.