  The Maxwell theory on non-commutative spaces has been considered. The
non-linear equations of electromagnetic fields on non-commutative spaces were
obtained in the compact spin-tensor (quaternion) form. It was shown that the
plane electromagnetic wave is the solution of the system of non-linear wave
equations of the second order for the electric and magnetic induction fields.
We have found the canonical and symmetrical energy-momentum tensors and their
non-zero traces. So, the trace anomaly of the energy-momentum tensor was
obtained in electrodynamics on non-commutative spaces. It was noted that the
dual transformations of electromagnetic fields on non-commutative spaces are
broken.
