On the nuclear dimension of strongly purely infinite C*-algebras

TL;DR

This paper proves that separable, nuclear, strongly purely infinite C*-algebras have a finite nuclear dimension, specifically at most three, based on a structural result by Kirchberg and Rordam.

Contribution

It establishes a universal upper bound of three on the nuclear dimension for this class of C*-algebras, linking structural properties to finite nuclear dimension.

Findings

Separable, nuclear, strongly purely infinite C*-algebras have nuclear dimension ≤ 3.

Utilizes a structural result by Kirchberg and Rordam on homotopy to zero.

Provides a key step towards classification of these algebras.

Abstract

We show that separable, nuclear and strongly purely infinite C*-algebras have finite nuclear dimension. In fact, the value is at most three. This exploits a deep structural result of Kirchberg and R{\o}rdam on strongly purely infinite C*-algebras that are homotopic to zero in an ideal-system preserving way.