2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78441We demonstrate the main idea of constructing irreducible unitary representations of Lie groups by using Fedosov deformation quantization in the concrete case of the group Aff(R) of affine transformations of the real straight line. By an exact computation of the star-product and the operator $\hat{\ell}_Z$, we show that the resulting representations exhausted all the irreducible representations of this groups.12 pages, LaTeX2e with AMS-Latex styleQuantum AlgebraRepresentation TheorySymplectic Geometry22E25, 22E45text