Symmetry via Lie algebra cohomology

Abstract

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.Comment: Conference proceedings: JARCS Sydney 2009 (The Australian-Japanese Workshop on Real and Complex Singularities held at the University of Sydney