The energy spectrum of an isotropic harmonic oscillator as a function of the noncommutativity parameter $\Theta$ is studied. It is shown that for a dense set of values of $\Theta$ the spectrum is degenerated and the algebra responsible for degeneracy can always be chosen to be SU(2). The generators of the algebra are constructed explicitly.

The systematic derivation of constants of the motion, based on Killing tensors and the gauge covariant approach, is outlined. Quantum dots are shown to support second-, third- and fourth-rank Killing tensors.