Abstract
A quantum deformation of the two-photon (or Schrodinger) Lie algebra is introduced in order to construct newn-dimensional classical Hamiltonian systems which have (n−2) functionally independent integrals of motion in involution; we say that such Hamiltonians define quasi-integrable systems. Furthermore, Hopf subalgebras of this quantum two-photon algebra (quantum extended 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.
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