  Five new families of noncommutative lightcones in 2+1 dimensions are
presented as the quantizations of the inequivalent Poisson homogeneous
structures that emerge when the lightcone is constructed as a homogeneous space
of the SO(2,1) conformal group. Each of these noncommutative lightcones
maintains covariance under the action of the respective quantum deformation of
the SO(2,1) conformal group. We discuss the role played by SO(2,1)
automorphisms in the classification of inequivalent Poisson homogeneous
lightcones, as well as the geometric aspects of this construction. The
localization properties of the novel quantum lightcones are analyzed and shown
to be deeply connected with the geometric features of the Poisson homogeneous
spaces.
