Extensions of pure C*-algebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908405753446400 |
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| author | Perera, Francesc Thiel, Hannes Vilalta, Eduard |
| author_facet | Perera, Francesc Thiel, Hannes Vilalta, Eduard |
| contents | Given a closed ideal $I$ in a C*-algebra $A$, we show that $A$ is pure if and only if $I$ and $A/I$ are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions.
As an application we show that stable multiplier algebras of reduced free group C*-algebras are pure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10529 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extensions of pure C*-algebras Perera, Francesc Thiel, Hannes Vilalta, Eduard Operator Algebras Primary 46L05, Secondary 19K14, 46L80, 46L85 Given a closed ideal $I$ in a C*-algebra $A$, we show that $A$ is pure if and only if $I$ and $A/I$ are pure. More generally, we study permanence of comparison and divisibility properties when passing to extensions. As an application we show that stable multiplier algebras of reduced free group C*-algebras are pure. |
| title | Extensions of pure C*-algebras |
| topic | Operator Algebras Primary 46L05, Secondary 19K14, 46L80, 46L85 |
| url | https://arxiv.org/abs/2506.10529 |