  The dynamical algebra of the q-deformed harmonic oscillator is constructed.
As a result, we find the free deformed Hamiltonian as well as the Hamiltonian
of the deformed oscillator as a complicated, momentum dependent interaction
Hamiltonian in terms of the usual canonical variables. Furthermore we construct
a well-defined algebra SU$_q$(1,1) with consistent conjugation properties and
comultiplication. We obtain non lowest weight representations of this algebra.
