A simple nuclear C*-algebra with an internal asymmetry

TL;DR

This paper constructs a simple approximately homogeneous C*-algebra demonstrating an internal asymmetry where its Elliott invariant admits an automorphism not arising from an algebra automorphism.

Contribution

It provides the first example of a simple AH algebra with an automorphism of its invariant not induced by an algebra automorphism.

Findings

Existence of a simple AH algebra with non-automorphism invariant automorphism

Demonstration of internal asymmetry in a nuclear C*-algebra

Insight into the relationship between algebra automorphisms and invariant automorphisms

Abstract

We construct an example of a simple approximately homogeneous C*-algebra such that its Elliott invariant admits an automorphism which is not induced by an automorphism of the algebra.