Simple AH algebras with the same Elliott invariant and radius of comparison

TL;DR

This paper constructs a large family of simple AH algebras that share the same Elliott invariant and radius of comparison but are distinguished by a local radius of comparison function, revealing new insights into their classification.

Contribution

It introduces a method to distinguish nonisomorphic AH algebras with identical invariants using a local radius of comparison function.

Findings

Uncountably many nonisomorphic AH algebras with identical invariants.

Distinction achieved via a local radius of comparison function.

Enhances understanding of classification invariants for AH algebras.

Abstract

We construct an uncountable family of pairwise nonisomorphic AH algebras with the same Elliott invariant and same radius of comparison. They can be distinguished by a local radius of comparison function, naturally defined on the positive cone of the K_0 group.