Lorentz shear modulus of a two-dimensional electron gas at high magnetic field

We show that the Lorentz shear modulus -- one of the three elastic moduli of a homogeneous electron gas in a magnetic field -- can be calculated exactly in the limit of high magnetic field (i.e. in the lowest Landau level). Its value is $\pm \hbar n/4$, where $n$ is the two-dimensional electron density and the sign is determined by the orientation of the magnetic field. We use this result to refine our previous calculations of the dispersion of the collective modes of fractional quantum Hall liquids.