[1004.4579] Generalized MICZ-Kepler system, duality, polynomial and deformed oscillator algebras:
"We present the quadratic algebra of the generalized MICZ-Kepler system in three-dimensional Euclidean space E3 and its dual the four dimensional singular oscillator in four-dimensional Euclidean space E4. We present their realization in terms of a deformed oscillator algebra using the Daskaloyannis construction. The structure constants are in these cases function not only of the Hamiltonian but also of other integrals commuting with all generators of the quadratic algebra. We also present a new algebraic derivation of the energy spectrum of the MICZ-Kepler system on the three sphere S3 using a quadratic algebra. These results point out also that results and explicit formula for structure functions obtained for quadratic, cubic and higher order polynomial algebras in context of two-dimensional superintegrable systems may be applied to superintegrable systems in higher dimensions with and without monopoles."
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