Nuclear dimension of simple 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.

arXiv commentInvent. Math., to appear. Minor changes, accepted version

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Cited by in corpus (35)

• Equivariant property (SI) revisited
• On classification of non-unital amenable simple C*-algebras, III, the range and the reduction
• The classification of Rokhlin flows on C*-algebras
• Uniform property Gamma
• The Cuntz-Toeplitz algebras have nuclear dimension one
• Alexandrov groupoids and the nuclear dimension of twisted groupoid ${\mathrm{C}}^{\ast }$-algebras
• Almost elementary étale groupoids
• The nuclear dimension of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• Amenable wreath products with non almost finite actions of mean dimension zero
• On tracial $\mathcal{Z}$-stability of simple non-unital C*-algebras
• Strict comparison for $C^{\ast }$-algebras arising from Almost finite groupoids
• Strongly outer actions of amenable groups on $\mathcal{Z}$-stable nuclear $C^{\ast }$-algebras
• Classification of ${\mathcal{O}}_{\infty }$-stable $C^{\ast }$-algebras
• Nuclear dimension of subhomogeneous twisted groupoid C*-algebras and dynamic asymptotic dimension
• Elementary amenability and almost finiteness
• Extensions of C*-algebas by a small ideal
• Nuclear dimension of graph C${}^{\ast }$-algebras with Condition~(K)
• A characterization of the Razak-Jacelon algebra
• Almost finiteness, comparison, and tracial $\mathcal{Z}$-stability
• Classification of tiling $C^{\ast }$-algebras
• Paper-folding models for the CAR algebra
• Decomposing nuclear maps
• On the possible temperatures for flows on an AF algebra
• Nuclear dimension of extensions of ${\mathcal{O}}_{\infty }$-stable algebras
• Nuclear dimension and virtually polycyclic groups
• C*-algebras and their nuclear dimension
• A geometric Elliott invariant and noncommutative rigidity of mapping tori
• The structure of crossed products by automorphisms of $C(X,D)$
• Rohlin actions of finite groups on the Razak-Jacelon algebra
• Constructions in minimal amenable dynamics and applications to the classification of ${\mathrm{C}}^{\ast }$-algebras
• Some properties for certain generalized tracial approximated ${\mathrm{C}}^{\ast }$-algebras
• Sturmian subshifts and their C*-algebras
• Equivariant property Gamma and the tracial local-to-global principle for C*-dynamics
• Classifiable ${\mathrm{C}}^{\ast }$-algebras from minimal $\mathbb{Z}$-actions and their orbit-breaking subalgebras
• The UCT problem for nuclear $C^{\ast }$-algebras