One-parameter continuous fields of Kirchberg algebras with rational K-theory

TL;DR

This paper proves that certain continuous fields of Kirchberg algebras with rational K-theory over the unit interval are classified by filtrated K-theory, extending classification results in operator algebras.

Contribution

It introduces a classification result for continuous fields of stable Kirchberg algebras with rational K-theory using filtrated K-theory.

Findings

Classification of continuous fields by filtrated K-theory

Applicable to algebras satisfying the UCT in KK-theory

Focus on algebras with rational K-theory groups

Abstract

We show that separable continuous fields over the unit interval whose fibers are stable Kirchberg algebras that satisfy the universal coefficient theorem in KK-theory and have rational K-theory groups are classified up to isomorphism by filtrated K-theory.