Classification of graph C*-algebras with no more than four primitive ideals

TL;DR

This paper reviews the current state of classifying graph C*-algebras that have up to four primitive ideals, summarizing recent progress and remaining challenges.

Contribution

It provides a comprehensive overview of the classification status for graph C*-algebras with limited primitive ideals, highlighting key results and open problems.

Findings

Classification completed for some subclasses

Remaining cases are still open

Framework for future research established

Abstract

We describe the status quo of the classification problem of graph C*-algebras with four primitive ideals or less.