  When the interaction potential is suitably reordered, the Moyal field theory
admits two types of Galilean symmetries, namely the conventional
mass-parameter-centrally-extended one with commuting boosts, but also the
two-fold centrally extended ``exotic'' Galilean symmetry, where the commutator
of the boosts yields the noncommutative parameter. In the free case, one gets
an ``exotic'' two-parameter central extension of the Schroedinger group. The
conformal symmetry is, however, broken by the interaction.
