A note on purely infinite corona algebras and extensions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918353317134336 |
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| author | Ng, Ping Wong Wang, Cangyuan |
| author_facet | Ng, Ping Wong Wang, Cangyuan |
| contents | Let $\mathcal{A}$ be a separable nuclear C*-algebra, and $\mathcal{B}$ be a nonunital separable simple $\mathcal{Z}$-stable C*-algebra. Continuing the work from Gabe-Lin-Ng, we classify all essential extensions, with large complement, of the form $$0 \rightarrow \mathcal{B} \rightarrow \mathcal{E} \rightarrow \mathcal{A} \rightarrow 0,$$ for the following cases: i. $\mathcal{C}(\mathcal{B})$ is properly infinite, and the extension is full. ii. $\mathcal{C}(\mathcal{B})$ is purely infinite (though not necessarily simple). We also have some more general results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20591 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A note on purely infinite corona algebras and extensions Ng, Ping Wong Wang, Cangyuan Operator Algebras Let $\mathcal{A}$ be a separable nuclear C*-algebra, and $\mathcal{B}$ be a nonunital separable simple $\mathcal{Z}$-stable C*-algebra. Continuing the work from Gabe-Lin-Ng, we classify all essential extensions, with large complement, of the form $$0 \rightarrow \mathcal{B} \rightarrow \mathcal{E} \rightarrow \mathcal{A} \rightarrow 0,$$ for the following cases: i. $\mathcal{C}(\mathcal{B})$ is properly infinite, and the extension is full. ii. $\mathcal{C}(\mathcal{B})$ is purely infinite (though not necessarily simple). We also have some more general results. |
| title | A note on purely infinite corona algebras and extensions |
| topic | Operator Algebras |
| url | https://arxiv.org/abs/2602.20591 |