  In this article we develop some elementary aspects of a theory of symmetry in
sub-Lorentzian geometry. First of all we construct invariants characterizing
isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize
vector fields which generate isometric and conformal symmetries in general
sub-Lorentzian manifolds. We then focus attention back to the case where the
underlying manifold is a contact 3 manifold and more specifically when the
manifold is also a Lie group and the structure is left-invariant.
