  Using the Moyal *-product and orthosymplectic supersymmetry, we construct a
natural non trivial supertrace and an associated non degenerate invariant
supersymmetric bilinear form for the Lie superalgebra structure of the Weyl
algebra. We decompose adjoint and twisted adjoint actions. We define a
renormalized supertrace and a formal inverse Weyl transform in a deformation
quantization framework and develop some examples.
