# Ergodic actions of compact groups on operator algebras: I. General theory

### Abstract

We introduce some general machinery for studying ergodic actions of compact groups on operator algebras, the most important tool being that of the multiplicity map. This theory is used subsequently in [42] to prove that a von Neumann algebra on which $\mathrm{SU}(2)$ acts ergodically is necessarily of Type I.

## Authors

Antony Wassermann