C*-algebras and their nuclear dimension

TL;DR

This paper reviews the concept of nuclear dimension in C*-algebras, highlighting its role as a non-commutative analogue of topological dimension, with examples and current research overview.

Contribution

It provides a comprehensive overview of nuclear dimension in C*-algebras, including examples and recent developments in the field.

Findings

Nuclear dimension generalizes topological dimension to non-commutative spaces.

Several key examples illustrate the concept.

The paper summarizes the current state of research in nuclear dimension.

Abstract

We review the notion of nuclear dimension for C*-algebras introduced by Winter and Zacharias. We explain why it is a non-commutative version of topological dimension. After presenting several examples, we give a brief overview of the state of the art.