Extensions ofC*-Algebras by a Small Ideal
| Autor: | Huaxin Lin, Ping Wong Ng |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | International Mathematics Research Notices. |
| ISSN: | 1687-0247 1073-7928 |
| DOI: | 10.1093/imrn/rnac115 |
| Popis: | We classify all essential extensions of the form $$ \begin{align*} &0 \rightarrow {\mathcal{W}} \rightarrow {D} \rightarrow A \rightarrow 0,\end{align*}$$where ${\mathcal {W}}$ is the unique separable simple C*-algebra with a unique tracial state, which is $KK$-contractible and has finite nuclear dimension, and $A$ is a separable amenable ${\mathcal {W}}$-embeddable C*-algebra, which satisfies the Universal Coefficient Theorem (UCT). We actually prove more general results. We also classify a class of amenable $C^*$-algebras, which have only one proper closed ideal ${\mathcal {W}}.$ |
| Databáze: | OpenAIRE |
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