# Nuclear dimension of simple C*-algebras

## TL;DR

This paper calculates the nuclear dimension of certain simple C*-algebras, enabling their classification and expanding the scope of the Elliott classification program to include more algebras related to group actions.

## Contribution

It provides the first computation of nuclear dimension for a broad class of Z-stable C*-algebras, linking classification to Z-stability.

## Key findings

- Nuclear dimension computed for separable, simple, unital, nuclear, Z-stable C*-algebras.
- Classification becomes feasible for large classes of C*-algebras from group actions.
- Expands the Elliott classification program to include new classes of C*-algebras.

## Abstract

We compute the nuclear dimension of separable, simple, unital, nuclear, Z-stable C*-algebras. This makes classification accessible from Z-stability and in particular brings large classes of C*-algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme.