Actions of discrete amenable groups on injective factors of type III_λ, λ≠1

Colin Eric Sutherland and Masamichi Takesaki

Vol. 137 (1989), No. 2, 405–444

DOI: 10.2140/pjm.1989.137.405

Abstract

Actions α of a discrete amenable group G on an injective factor ℳ of type III_λ, λ≠1, are classified up to cocycle conjugacy in terms of the module mod (α), the characteristic invariant χ_α and the modular invariant ν_α of α. These invariants live on the flow of weights. It is also shown that each element of H¹(ℱ(ℳ)), the first cohomology group of the flow of weights, has a C^∞-representative cocycle.

Mathematical Subject Classification 2000

Primary: 46L40

Secondary: 22D25, 46L10, 46L55

Milestones

Received: 24 September 1987

Published: 1 April 1989