Abstract

In this last article of the series on outer actions of a countable discrete amenable group on approximately finite-dimensional factors, we analyze outer actions of a countable discrete free abelian group on an approximately finite-dimensional factor of type III_λ with 0 < λ < 1 and compute outer conjugacy invariants. As a byproduct, we discover the asymmetrization technique for coboundary condition on a T-valued cocycle of a torsion-free abelian group, which might have been known by group cohomologists. As the asymmetrization technique gives us a very handy criteria for coboundaries, we present it here in detail.

Keywords

outer action, outer conjugacy, cohomology of group, asymmetrization

Mathematical Subject Classification

Primary: 46L55

Secondary: 46L35, 46L40, 20J06

Milestones

Received: 4 June 2009
Accepted: 11 June 2009

Authors