2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56594We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \emph{do not} use any kind of semiclassic approximation or limiting procedures for $\hbar \to 0$. Harmonic oscillator considered within the approach. Keywords: Classic and quantum mechanics, Hamilton and Heisenberg equations, Poisson brackets, commutator, Heisenberg group.LaTeX2e, 16 pages; added subsection with an exampleMathematical PhysicsFunctional AnalysisQuantum AlgebraRepresentation TheoryClassical PhysicsQuantum Physics81R05; 81P05, 22E70, 43A65text