Abstract
We develop a theory of extensions of von Neumann algebras by locally compact groups of automorphisms. The emphasis is on the description (from an algebraic point of view) of those extensions of a given von Neumann algebra by a given group which determine a fixed homomorphism from the group into the outer automorphism classes of the given algebra. Thus the study of such homomorphisms occupies a substantial part of the paper; for a large class of examples we are able to determine when such a homomorphism is split, and give a simple algebraic description of the extensions. We then give necessary and sufficient conditions (of an analytic nature) for an extension to be equivalent to a twisted crossed product extension, and give some applications to the study of representations of certain topological groups, and to approximately finite dimensional von Neumann algebras.
