  Several physical systems (two identical particles in two dimensions,
isotropic oscillator and Kepler system in a 2-dim curved space) and
mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm
W}_0$) are shown to posses the structure of a generalized deformed su(2)
algebra, the representation theory of which is known. Furthermore, the
generalized deformed parafermionic oscillator is identified with the algebra of
several physical systems (isotropic oscillator and Kepler system in 2-dim
curved space, Fokas--Lagerstrom, Smorodinsky--Winternitz and Holt potentials)
and mathematical constructions (generalized deformed su(2) algebra, finite W
algebras $\bar {\rm W}_0$ and W$_3^{(2)}$). The fact that the Holt potential is
characterized by the W$_3^{(2)}$ symmetry is obtained as a by-product.
