A class of AF-algebras up to universal UHF-algebra stability

TL;DR

This paper classifies a specific class of AF-algebras up to tensoring with the universal UHF-algebra using trace spaces, simplifying their classification.

Contribution

It introduces a classification result for certain AF-algebras based solely on their trace spaces after tensoring with the universal UHF-algebra.

Findings

AF-algebras with non-converging Bratteli diagrams are classified by trace spaces

Tensoring with the universal UHF-algebra preserves classification

Trace space determines isomorphism after tensoring

Abstract

We will show that separable unital AF-algebras whose Bratteli diagrams do not allow converging two nodes into one node, can be classified up to the tensor product with the universal UHF-algebra $\Q$ only by their trace spaces. That is, if $\A$ and $\B$ are such AF-algebras, then $T(A)=T(B)$ if and only if $\A\otimes \Q \cong \B\otimes \Q$.