Amenability and exactness for dynamical systems and their C*-algebras

TL;DR

This survey explores how properties like amenability and exactness in C*-dynamical systems influence the structure and nuclearity of their crossed product C*-algebras.

Contribution

It systematically analyzes the relationships between amenability, nuclearity, and exactness in the context of C*-dynamical systems and their crossed products.

Findings

Amenability implies certain nuclearity conditions in crossed products.

Exactness of systems correlates with exactness of their crossed products.

The survey clarifies the conditions under which these properties are equivalent or imply each other.

Abstract

In this survey, we study the relations between amenability (resp. amenability at infinity) of C*-dynamical systems and equality or nuclearity (resp. exactness) of the corresponding crossed products.