  We study the dynamical symmetries of a class of two-dimensional
superintegrable systems on a 2-sphere, obtained by a procedure based on the
Marsden-Weinstein reduction, by considering its shape-invariant intertwining
operators. These are obtained by generalizing the techniques of factorization
of one-dimensional systems. We firstly obtain a pair of noncommuting Lie
algebras $su(2)$ that originate the algebra $so(4)$. By considering three
spherical coordinate systems we get the algebra $u(3)$ that can be enlarged by
`reflexions' to $so(6)$. The bounded eigenstates of the Hamiltonian hierarchies
are associated to the irreducible unitary representations of these dynamical
algebras.
