## Proceedings of the Centre for Mathematics and its Applications

- Proc. Centre Math. Appl.
- Miniconference on Harmonic Analysis and Operator Algebras. M. Cowling, C. Meaney, and W. Moran, eds. Proceedings of the Centre for Mathematical Analysis, v. 16. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1987), 317 - 328

### Classifying actions of groups on von Neumann algebras

#### Abstract

The objective of this paper is to provide an overview of results obtained recently by the author and M. Takesaki on the classification, up to cocycle conjugacy, of actions of discrete amenable groups on injective factor von Neumann algebras of type $III_{\lambda}, \lambda \neq 1$. Details will appear elsewhere, [14]. We also describe the conclusions of preceding work of Oceanu, [10] extending previous work of Connes [1], [2] and Jones [7], and of Sutherland and Takesaki, [13], on actions of discrete amenable groups and groupoids on injective semi finite von Neumann algebras.

#### Article information

**Dates**

First available in Project Euclid:
18 November 2014

**Permanent link to this document**

https://projecteuclid.org/
euclid.pcma/1416336226

**Mathematical Reviews number (MathSciNet)**

MR954008

#### Citation

Sutherland, Colin E. Classifying actions of groups on von Neumann algebras. Miniconference on Harmonic Analysis and Operator Algebras, 317--328, Centre for Mathematical Analysis, The Australian National University, Canberra AUS, 1987. https://projecteuclid.org/euclid.pcma/1416336226