Freeness of actions of finite groups on C*-algebras

TL;DR

This paper reviews various notions of freeness for finite group actions on C*-algebras, analyzing their properties, strengths, weaknesses, and interrelations within noncommutative geometry.

Contribution

It systematically compares different freeness conditions for finite group actions on C*-algebras, clarifying their relationships and applications.

Findings

Rokhlin property and its variants are central to understanding freeness.

Different freeness notions have distinct strengths and limitations.

The paper highlights the connections between these properties and their implications.

Abstract

We describe some of the forms of freeness of group actions on noncommutative C*-algebras that have been used, with emphasis on actions of finite groups. We give some indications of their strengths, weaknesses, applications, and relationships to each other. The properties discussed include the Rokhlin property, K-theoretic freeness, the tracial Rokhlin property, pointwise outerness, saturation, hereditary saturation, and the requirement that the strong Connes spectrum be the entire dual.