\mathcal Z-stability of C(X)\rtimesΓ

2020/08/07 by Zhuang Niu, Niu, Zhuang
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2008.03357

openalex publication_date 2020/08/07 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Let (X, Γ) be a free and minimal topological dynamical system, where X is a separable compact Hausdorff space and Γ is a countable infinite discrete amenable group. It is shown that if (X, Γ) has the Uniform Rokhlin Property and Cuntz comparison of open sets, then mdim(X, Γ)=0 implies that (C(X) \rtimesΓ)⊗\mathcal Z ≅ C(X) \rtimesΓ, where mdim is the mean dimension and \mathcal Z is the Jiang-Su algebra. In particular, in this case, mdim(X, Γ)=0 implies that the C*-algebra C(X) \rtimesΓ is classified by the Elliott invariant.

Citations

• Trace spaces of simple nuclear C*-algebras with finite-dimensional extreme boundary
• Mean topological dimension

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