  We study algebraic structures underlying 't Hooft's construction relating
classical systems with the quantum harmonic oscillator. The role of group
contraction is discussed. We propose the use of SU(1,1) for two reasons:
because of the isomorphism between its representation Hilbert space and that of
the harmonic oscillator and because zero point energy is implied by the
representation structure. Finally, we also comment on the relation between
dissipation and quantization.
