2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/217298Developing a non-compact version of the SUSY Hopf map, we formulate the quantum Hall effect on a super-hyperboloid. Based on $OSp(1|2)$ group theoretical methods, we first analyze the one-particle Landau problem, and successively explore the many-body problem where Laughlin wavefunction, hard-core pseudo-potential Hamiltonian and topological excitations are derived. It is also shown that the fuzzy super-hyperboloid emerges in the lowest Landau level.14 pages, two columns, no figures, published version, typos correctedHigh Energy Physics - TheoryMesoscale and Nanoscale PhysicsMathematical Physicstext