Every countable group admits amenable actions on stably finite simple C*-algebras

TL;DR

This paper constructs explicit examples of non-amenable groups acting amenably on stably finite simple C*-algebras, using the full Fock space and trace-scaling automorphisms.

Contribution

It provides the first explicit constructions of amenable actions for any countable group on stably finite simple C*-algebras, expanding understanding of group actions in operator algebras.

Findings

First examples of non-amenable groups with amenable actions on stably finite simple C*-algebras

Explicit construction method using full Fock space and trace-scaling automorphisms

Demonstrates new interactions between group theory and operator algebra structures

Abstract

We give the first examples of (non-amenable group) amenable actions on stably finite simple C*-algebras. More precisely, we give such actions for any countable group in an explicit way. The main ingredients of our construction are the full Fock space of the regular representation and a trace-scaling automorphism.