C*-algebras and their 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.

arXiv comment23 pages; minor revision. Contemp. Math. to appear

References in corpus (6)

• Completely positive maps of order zero
• Nuclear dimension of simple C*-algebras
• Classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras
• Nuclear dimension, Z-stability, and algebraic simplicity for stably projectionless C*-algebras
• The nuclear dimension of C*-algebras associated to homeomorphisms
• The nuclear dimension of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras