The UCT problem for nuclear $C^{\ast }$-algebras

Abstract

In recent years, a large class of nuclear $C^{\ast }$-algebras have been classified, modulo an assumption on the Universal Coefficient Theorem (UCT). We think this assumption is redundant and propose a strategy for proving it. Indeed, following the original proof of the classification theorem, we propose bridging the gap between reduction theorems and examples. While many such bridges are possible, various approximate ideal structures appear quite promising.

arXiv comment13 pages; to appear in the Rocky Mountain Journal of Mathematics

References in corpus (6)

• Nuclear dimension of simple C*-algebras
• Classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras
• A classification of finite simple amenable Z-stable C*-algebras, II, --C*-algebras with rational generalized tracial rank one
• Controlled KK-theory, and a Milnor exact sequence
• Approximate ideal structures and K-theory
• Graph-Based Models for Kirchberg Algebras