  The Wigner-Weyl isomorphism for quantum mechanics on a compact simple Lie
group $G$ is developed in detail. Several New features are shown to arise which
have no counterparts in the familiar Cartesian case. Notable among these is the
notion of a `semiquantised phase space', a structure on which the Weyl symbols
of operators turn out to be naturally defined and, figuratively speaking,
located midway between the classical phase space $T^*G$ and the Hilbert space
of square integrable functions on $G$. General expressions for the star product
for Weyl symbols are presented and explicitly worked out for the angle-angular
momentum case.
