Kirchberg X-algebras with real rank zero and intermediate cancellation

TL;DR

This paper develops a classification framework for certain C*-algebras over finite T_0-spaces with specific properties, using a universal coefficient theorem and range results, advancing understanding of their structure and extensions.

Contribution

It proves a universal coefficient theorem for C*-algebras over finite T_0-spaces with vanishing boundary maps and classifies unital/stable real-rank-zero Kirchberg X-algebras with intermediate cancellation.

Findings

Universal coefficient theorem established for these C*-algebras.

Complete classification achieved under bootstrap assumptions.

Range results obtained for specific graph and Cuntz-Krieger algebras with intermediate cancellation.

Abstract

A universal coefficient theorem is proved for C*-algebras over an arbitrary finite T_0-space X which have vanishing boundary maps. Under bootstrap assumptions, this leads to a complete classification of unital/stable real-rank-zero Kirchberg X-algebras with intermediate cancellation. Range results are obtained for (unital) purely infinite graph C*-algebras with intermediate cancellation and Cuntz-Krieger algebras with intermediate cancellation. Permanence results for extensions of these classes follow.