The extension problem for graph $C^*$-algebras

TL;DR

This paper provides a comprehensive K-theoretical characterization of when extensions of simple graph C*-algebras result in a graph C*-algebra, advancing understanding of their structural properties.

Contribution

It offers a complete K-theoretical criterion for identifying when extensions of simple graph C*-algebras are themselves graph C*-algebras.

Findings

Complete K-theoretical description for extensions

Criteria for extensions to be graph C*-algebras

Advances understanding of graph C*-algebra extensions

Abstract

We give a complete $K$-theoretical description of when an extension of two simple graph $C^{*}$-algebras is again a graph $C^{*}$-algebra.