Nonlocal dynamics and infinite non-relativistic conformal symmetries

We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the non-relativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model and on the quantum level it leads to the centrally extended Virasoro algebra.