  We present a class of photonic lattices with an underlying symmetry given by
a finite-dimensional representation of the 2+1D Lorentz group. In order to
construct such a finite-dimensional representation of a non-compact group, we
have to design a $\mathcal{PT}$-symmetric optical structure. Thus, the array of
coupled waveguides may keep or break $\mathcal{PT}$-symmetry, leading to a
device that behaves like an oscillator or directional amplifier, respectively.
We show that the so-called linear $\mathcal{PT}$-symmetric dimer belongs to
this class of photonic lattices.
