Vol. 137, No. 2, 1989

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Actions of discrete amenable groups on injective factors of type IIIλ, λ1

Colin Eric Sutherland and Masamichi Takesaki

Vol. 137 (1989), No. 2, 405–444
Abstract

Actions α of a discrete amenable group G on an injective factor of type IIIλ, λ1, are classified up to cocycle conjugacy in terms of the module mod (α), the characteristic invariant χα and the modular invariant να of α. These invariants live on the flow of weights. It is also shown that each element of H1(()), 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
Authors
Colin Eric Sutherland
Masamichi Takesaki