The equations of pre-metric electromagnetism are formulated as an exterior
differential system on the bundle of exterior differential 2-forms over the
spacetime manifold. The general form for the symmetry equations of the system
is computed and then specialized to various possible forms for an
electromagnetic constitutive law, namely, uniform linear, non-uniform linear,
and uniform nonlinear. It is shown that in the uniform linear case, one has
four possible ways of prolonging the symmetry Lie algebra, including
prolongation to a Lie algebra of infinitesimal projective transformations of a
real four-dimensional projective space. In the most general non-uniform linear
case, th effect of non-uniformity on symmetry seems inconclusive in the absence
of further specifics, and in the uniform nonlinear case, the overall difference
from the uniform linear case amounts to a deformation of the electromagnetic
constitutive tensor by the electromagnetic fields strengths, which induces a
corresponding deformation of the symmetry Lie algebra that was obtained in the
uniform linear case.Comment: 53 pages. Annalen der Physik (Leipzig) (2005), to be publishe
