On the classification problem for nuclear C*-algebras

TL;DR

This paper constructs a specific nuclear C*-algebra with unique shape and trace properties that distinguish it from its tensor products, challenging existing classification assumptions.

Contribution

It introduces a simple, unital AH algebra with shape and trace invariants matching its tensor products but not isomorphic to them, providing new insights into classification.

Findings

Constructed a nuclear C*-algebra with shape equivalent to its tensor product

Showed the algebra has the same tracial simplex as its tensor product

Proved the algebra is not isomorphic to its tensor product

Abstract

We construct a simple, unital AH algebra which is shape equivalent to its tensor product with any infinite-dimensional UHF algebra, has the same tracial simplex as the said tensor product, and yet is not isomorphic to it. An analogous result for automorphisms is also proved.