  The symmetrized product for quantum mechanical observables is defined. It is
seen as consisting of the ordinary multiplication and the application of the
superoperator that orders the operators of coordinate and momentum. This
superoperator is defined in a way that allows obstruction free quantization
when the observables are considered from the point of view of the algebra.
Then, the operatorial version of the Poisson bracket is defined. It is shown
that it has all properties of the Lie bracket and that it can substitute the
commutator in the von Neumann equation.
