2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185537Quantum Mechanics in the non-commutative plane is shown to admit the ``exotic'' symmetry of the doubly-centrally-extended Galilei group. When coupled to a planar magnetic field whose strength is the inverse of the non-commutative parameter, the system becomes singular, and ``Faddeev-Jackiw'' reduction yields the ``Chern-Simons'' mechanics of Dunne, Jackiw, and Trugenberger. The reduced system moves according to the Hall law.Revised version. The formula for the conserved quantities is corrected; some more references added. 11 pages, LaTex, no figuresHigh Energy Physics - TheoryCondensed Mattertext