Abstract
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 emphasized to produce the noncommuting structure that occurs when an electron is subjected to a constant magnetic field and Berry curvature.
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