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.
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机译：示出了几个物理系统（二维中两个相同的粒子，在2维弯曲空间中的各向同性振荡器和开普勒系统）和数学结构（二次代数QH（3），有限W代数\ bar {\ rm W} _0）拥有广义变形su（2）代数的结构，其表示理论是已知的。此外，广义变形的超铁离子振荡器是由几个物理系统（2-dim弯曲空间中的各向同性振荡器和开普勒系统，Fokas-Lagerstrom，Smorodinsky-Winternitz和Holt势）的代数和数学结构（广义变形su（ 2）代数，有限W代数\ bar {\ rm W} _0和W_3 ^ {（2）}）。作为副产物获得了霍尔特势以W_3 ^ {（2）}对称性为特征的事实。
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