Quasi-integrable and superintegrable systems from a 'deformed-mass' two-photon algebra

A quantum deformation of the two-photon (or Schrodinger) Lie algebra is int roduced in order to construct new n-dimensional classical Hamiltonian syste ms which have (n - 2) functionally independent integrals of motion in invol ution; we say that such Hamiltonians define quasi-integrable systems. Furth ermore, Hopf subalgebras of this quantum two-photon algebra (quantum extend ed Galilei and harmonic oscillator algebras) provide another set of (n - 1) integrals of motion for Hamiltonians defined on these Hopf subalgebras, so that they lead to superintegrable systems.