Exotic circle actions on classifiable C*-algebras

TL;DR

This paper constructs a specific example of a simple, nuclear, Z-stable C*-algebra with a circle action whose crossed product is simple but not Z-stable, challenging assumptions about stability properties.

Contribution

It provides the first known example of a circle action on a classifiable C*-algebra resulting in a non-Z-stable crossed product.

Findings

Crossed product is simple but not Z-stable

Example challenges existing stability assumptions

Advances understanding of circle actions on C*-algebras

Abstract

We construct an example of a simple nuclear separable unital stably finite Z-stable C*-algebra along with an action of the circle such that the crossed product is simple but not Z-stable.