  Crawley-Boevey introduced the definition of a noncommutative Poisson
structure on an associative algebra A that extends the notion of the usual
Poisson bracket. Let V be a symplectic manifold and G be a finite group of
symplectimorphisms of V. Consider the twisted group algebra A=C[V]#G.
  We produce a counterexample to prove that it is not always possible to define
a noncommutative poisson structure on C[V]#G that extends the Poisson bracket
on C[V]^G.
