2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63492We present the q-deformed counterpart of the local representations of the (1+1) extended Galilei group. These representations act on the space of wavefunctions defined in the space-time. As in the classical case the q-local representations are reducible and the condition of irreducibility is given by the q-Casimir equation that in the limit of the deformation parameter going to zero becomes the Schroedinger equation of a free particle.LaTeX, 11 pagesQuantum AlgebraMathematical Physics17B37, 81R50text