Coloured Isomorphism of Classifiable C*-algebras

TL;DR

This paper demonstrates that for a specific class of well-behaved C*-algebras, their coloured isomorphism class is uniquely determined by their tracial simplex, linking algebraic structure to trace space.

Contribution

It establishes that the coloured isomorphism class of unital, simple, $ ext{Z}$-stable, separable amenable C*-algebras satisfying UCT is fully characterized by their tracial simplex.

Findings

Coloured isomorphism class determined by tracial simplex

Applicable to unital, simple, $ ext{Z}$-stable, separable amenable C*-algebras satisfying UCT

Provides a classification result linking algebraic and trace data

Abstract

It is shown that the coloured isomorphism class of a unital, simple, $\mathcal{Z}$-stable, separable amenable C$^*$-algebra satisfying the Universal Coefficient Theorem (UCT) is determined by its tracial simplex.