Nuclear dimension of extensions of commutative C*-algebras by Kirchberg algebras

TL;DR

This paper calculates the nuclear dimension of certain C*-algebra extensions involving commutative quotients and Kirchberg ideals, linking algebraic properties to graph structures.

Contribution

It provides a method to determine the nuclear dimension for extensions with commutative quotients and Kirchberg ideals, connecting algebraic and graph-theoretic concepts.

Findings

Identified the nuclear dimension for specific C*-algebra extensions.

Connected the algebraic structure to finite directed graphs.

Provided criteria for when C*-algebras are covered by the theorem.

Abstract

We compute the nuclear dimension of extensions of C*-algebras involving commutative unital quotients and stable Kirchberg ideals. We identify the finite directed graphs whose C*-algebras are covered by this theorem.