  The representations of Galilean generators are constructed on a space where
both position and momentum coordinates are noncommutating operators. A
dynamical model invariant under noncommutative phase space transformations is
constructed. The Dirac brackets of this model reproduce the original
noncommutative algebra. Also, the generators in terms of noncommutative phase
space variables are abstracted from this model in a consistent manner. Finally,
the role of Jacobi identities is emphasised to produce the noncommuting
structure that occurs when an electron is subjected to a constant magnetic
field and Berry curvature.
