  A class of quantum superintegrable Hamiltonians defined on a two-dimensional
hyperboloid is considered together with a set of intertwining operators
connecting them. It is shown that such intertwining operators close a su(2,1)
Lie algebra and determine the Hamiltonians through the Casimir operators. By
means of discrete symmetries a broader set of operators is obtained closing a
so(4,2) algebra. The physical states corresponding to the discrete spectrum of
bound states as well as the degeneration are characterized in terms of unitary
representations of su(2,1) and so(4,2).
