Centrally pure C*-algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914209745338368 |
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| author | Perera, Francesc Thiel, Hannes Vilalta, Eduard |
| author_facet | Perera, Francesc Thiel, Hannes Vilalta, Eduard |
| contents | We show that a separable C*-algebra $A$ is $\mathcal{Z}$-stable if and only if its uncorrected central sequence algebra $A' \cap A_{\mathcal{U}}$ is pure, if and only if Kirchberg's central sequence algebra $F(A)$ is pure.
More generally, we show that a C*-algebra $A$ is separably $\mathcal{Z}$-stable if and only if the relative central sequence algebra $B' \cap A_{\mathcal{U}}$ is pure for every separable subalgebra $B \subseteq A_{\mathcal{U}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_17261 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Centrally pure C*-algebras Perera, Francesc Thiel, Hannes Vilalta, Eduard Operator Algebras Primary 46L05, Secondary 19K14, 46L80, 46L85 We show that a separable C*-algebra $A$ is $\mathcal{Z}$-stable if and only if its uncorrected central sequence algebra $A' \cap A_{\mathcal{U}}$ is pure, if and only if Kirchberg's central sequence algebra $F(A)$ is pure. More generally, we show that a C*-algebra $A$ is separably $\mathcal{Z}$-stable if and only if the relative central sequence algebra $B' \cap A_{\mathcal{U}}$ is pure for every separable subalgebra $B \subseteq A_{\mathcal{U}}$. |
| title | Centrally pure C*-algebras |
| topic | Operator Algebras Primary 46L05, Secondary 19K14, 46L80, 46L85 |
| url | https://arxiv.org/abs/2512.17261 |