Classification of equivariantly $\mathcal{O}_2$-stable amenable actions on nuclear $\mathrm{C}^\ast$-algebras
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929499354955776 |
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| author | Pagliero, Matteo Szabó, Gábor |
| author_facet | Pagliero, Matteo Szabó, Gábor |
| contents | Given a second-countable, locally compact group $G$, we consider amenable $G$-actions on separable, stable, nuclear $\mathrm{C}^\ast$-algebras that are isometrically shift-absorbing and tensorially absorb the trivial action on the Cuntz algebra $\mathcal{O}_2$. We show that such actions are classified up to cocycle conjugacy by the induced $G$-action on the primitive ideal space. In the special case when $G$ is exact, we prove a unital version of our classification theorem. For compact groups, we obtain a classification up to conjugacy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_12472 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Classification of equivariantly $\mathcal{O}_2$-stable amenable actions on nuclear $\mathrm{C}^\ast$-algebras Pagliero, Matteo Szabó, Gábor Operator Algebras 46L55, 46L35 Given a second-countable, locally compact group $G$, we consider amenable $G$-actions on separable, stable, nuclear $\mathrm{C}^\ast$-algebras that are isometrically shift-absorbing and tensorially absorb the trivial action on the Cuntz algebra $\mathcal{O}_2$. We show that such actions are classified up to cocycle conjugacy by the induced $G$-action on the primitive ideal space. In the special case when $G$ is exact, we prove a unital version of our classification theorem. For compact groups, we obtain a classification up to conjugacy. |
| title | Classification of equivariantly $\mathcal{O}_2$-stable amenable actions on nuclear $\mathrm{C}^\ast$-algebras |
| topic | Operator Algebras 46L55, 46L35 |
| url | https://arxiv.org/abs/2309.12472 |