Sharing symmetries in non-linear systems: Generalized Heisenberg–Weyl algebra on the de Sitter space-time out of the sphere S3

In this paper, we exploit the formal equivalence of Solution Manifold two distinct physical systems to create enough symmetries so as characterize them by Noether Invariants, thus favoring their future quantization. doing, somehow generalize Arnold Transformation for non-necessarily linear systems. Very particularly, algorithm applies case motion on de Sitter space-time providing a finite-dimensional algebra generalizing Heisenberg–Weyl globally. case, basic (contact) symmetry is imported from (non-relativistic) particle sphere [Formula: see text].