2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/186404In order to assess possible observable effects of noncommutativity in deformations of quantum mechanics, all irreducible representations of the noncommutative Heisenberg algebra and Weyl-Heisenberg group on the two-torus are constructed. This analysis extends the well known situation for the noncommutative torus based on the algebra of the noncommuting position operators only. When considering the dynamics of a free particle for any of the identified representations, no observable effect of noncommutativity is implied.24 pages, no figuresHigh Energy Physics - Theorytext