Every classifiable simple C*-algebra has a Cartan subalgebra

Abstract

We construct Cartan subalgebras in all classifiable stably finite C*-algebras. Together with known constructions of Cartan subalgebras in all UCT Kirchberg algebras, this shows that every classifiable simple C*-algebra has a Cartan subalgebra.

final version, accepted for publication in Invent. Math.; title changed, results improved; 29 pages

References in corpus (9)

• Classification of finite simple amenable $\mathcal{Z}$-stable $C^{\ast }$-algebras
• On classification of simple non-unital amenable C*-algebras, II
• Cartan subalgebras and the UCT problem, II
• On classification of non-unital simple amenable C*-algebras, I
• The classification of simple separable KK-contractible C*-algebras with finite nuclear dimension
• Simple stably projectionless C*-algebras with generalized tracial rank one
• Groupoid Models of $C^{\ast }$-algebras and Gelfand Duality
• Approaching the UCT problem via crossed products of the Razak-Jacelon algebra
• Graph-Based Models for Kirchberg Algebras

Cited by in corpus (2)

• Limit operator theory for groupoids
• Classifiable ${\mathrm{C}}^{\ast }$-algebras from minimal $\mathbb{Z}$-actions and their orbit-breaking subalgebras