  The Killing operator on a Riemannian manifold is a linear differential
operator on vector fields whose kernel provides the infinitesimal Riemannian
symmetries. The Killing operator is best understood in terms of its
prolongation, which entails some simple tensor identities. These simple
identities can be viewed as arising from the identification of certain Lie
algebra cohomologies. The point is that this case provides a model for more
complicated operators similarly concerned with symmetry.
