Abstract
We study twisted crossed products of von Neumann algebras by locally compact groups of automorphisms, where the twist is measured by a two-cocycle on the group, with values in the unitary group in the centre of the algebra. After examining alternative definitions of the crossed product, we prove the existence of “dual weights” on the crossed product, and identify the modular objects associated with these dual weights. We give criteria under which an automorphism of the original algebra may be lifted to an automorphism of the crossed product, and prove conditions under which the twisted crossed product will coincide with an ordinary crossed product. We give examples; some arising from extension theory of abelian groups, and the others giving a construction of factors not anti-isomorphic with themselves.
