Amenable actions on ill-behaved simple C*-algebras

TL;DR

This paper constructs the first known examples of amenable group actions on certain simple nuclear C*-algebras that are neither stably finite nor purely infinite, expanding understanding of their structure.

Contribution

It combines existing constructions to produce new examples of amenable actions on simple C*-algebras with specific properties, including unital cases for free groups.

Findings

First examples of amenable actions on non-amenable groups on simple nuclear C*-algebras

Crossed products remain simple with finite and infinite projections

Includes unital examples for free groups

Abstract

By combining R{\o}rdam's construction and the author's previous construction, we provide the first examples of amenable actions of non-amenable groups on simple separable nuclear C*-algebras that are neither stably finite nor purely infinite. For free groups, we also provide unital examples. We arrange the actions so that the crossed products are still simple with both a finite and an infinite projection.