Quantum and classical brackets

We describe p-mechanical (Kisil, V. V. (1996). Journal of Natural Geometry 9(l), 1-14; Kisil, V. V. (1999). Advances in Mathematics 147(l), 35-73; Prezhdo, O. V. and Kisil, V. V. (1997). Physical Review A 56(l), 162-175) brackets that generate quantum (commutator) and classical (Poisson) brackets in corresponding representations of the Heisenberg group. We do not use any kind of semiclassical approximation or limiting procedure for h --> 0.