  A set of recent results indicates that fractionally filled bands of Chern
insulators in two dimensions support fractional quantum Hall states analogous
to those found in fractionally filled Landau levels. We provide an
understanding of these results by examining the algebra of Chern band projected
density operators. We find that this algebra closes at long wavelengths and for
constant Berry curvature, whereupon it is isomorphic to the W-Infinity algebra
of lowest Landau level projected densities first identified by Girvin,
MacDonald and Platzman [Phys. Rev. B 33, 2481 (1986).] For Hamiltonians
projected to the Chern band this provides a route to replicating lowest Landau
level physics on the lattice.
