  It is well known that noncommutative geometry naturally emerges in the
quantum Hall states due to the presence of strong and constant magnetic fields.
Here, we discuss the underlying noncommutative geometry of quantum Hall fluids
in which the magnetic fields are spatially inhomogenoeus. We analyze these
cases by employing symplectic geometry and Fedosov's deformation quantization,
which rely on symplectic connections and Fedosov star-product. Through this
formalism, we unveil some new features concerning the static limit of the
Haldane's unimodular metric and the Girvin-MacDonald-Platzman algebra of the
density operators, which plays a central role in the fractional quantum Hall
effect.
