The nuclear dimension of graph C*-algebras

TL;DR

This paper determines the nuclear dimension of certain graph C*-algebras, showing it is 1 when the ideal has finitely many ideals and either 1 or 2 when infinitely many, depending on the structure.

Contribution

It establishes the nuclear dimension for a class of graph C*-algebras based on ideal structure, extending previous results in the field.

Findings

Nuclear dimension of C*(E) is 1 when I has finitely many ideals.

Nuclear dimension is 1 or 2 when I has infinitely many ideals.

Provides a classification of nuclear dimension based on ideal properties.

Abstract

Consider a graph C*-algebra C*(E) with a purely infinite ideal I (possibly all of C*(E)) such that I has only finitely many ideals and C*(E)/I is approximately finite dimensional. We prove that the nuclear dimension of C*(E) is 1. If I has infinitely many ideals, then the nuclear dimension of C*(E) is either 1 or 2.