Reduction of filtered K-theory and a characterization of Cuntz-Krieger algebras

TL;DR

This paper demonstrates that for certain C*-algebras, a simplified invariant suffices to classify them, and it characterizes a specific class of Cuntz-Krieger algebras using this invariant.

Contribution

It introduces a smaller invariant equivalent to filtered K-theory for real-rank-zero C*-algebras and characterizes purely infinite Cuntz-Krieger algebras with accordion space primitive ideals.

Findings

Filtered K-theory is equivalent to a smaller invariant for specified C*-algebras.

Characterization of purely infinite Cuntz-Krieger algebras with accordion space primitive ideal space.

Abstract

We show that filtered K-theory is equivalent to a substantially smaller invariant for all real-rank-zero C*-algebras with certain primitive ideal spaces -- including the infinitely many so-called accordion spaces for which filtered K-theory is known to be a complete invariant. As a consequence, we give a characterization of purely infinite Cuntz-Krieger algebras whose primitive ideal space is an accordion space.