  We discuss the linear hydrodynamic response of a two-dimensional active
chiral compressible fluid with odd viscosity. The viscosity coefficient
represents broken time-reversal and parity symmetries in the 2D fluid and
characterizes the deviation of the system from a passive fluid. Taking into
account the hydrodynamic coupling to the underlying bulk fluid, we obtain the
odd viscosity-dependent mobility tensor, which is responsible for the
non-reciprocal hydrodynamic response to a point force. Furthermore, we consider
a finite-size disk moving laterally in the 2D fluid and demonstrate that the
disk experiences a non-dissipative lift force in addition to the dissipative
drag one.
