Superintegrable Deformations of the Smorodinsky–Winternitz Hamiltonian

A constructive procedure to obtain superintegrable deformations of the classical Smorodinsky–Winternitz Hamiltonian by using quantum deformations of its underlying Poisson sl(2) coalgebra symmetry is introduced. Through this example, the general connection between coalgebra symmetry and quasi-maximal superintegrability is analysed. The notion of comodule algebra symmetry is also shown to be applicable in order to construct new integrable deformations of certain Smorodinsky–Winternitz systems. Published in Superintegrability in Classical and Quantum Systems, edited by P. Tempesta, P. Winternitz, J. Harnad, W. Miller Jr., G. Pogosyan and M.A. Rodŕıguez, CRM Proceedings & Lecture Notes, vol. 37, American Mathematical Society, 2004 1 2