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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.16759 |
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| _version_ | 1866918030877917184 |
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| author | Bassi, Jacopo Conti, Roberto |
| author_facet | Bassi, Jacopo Conti, Roberto |
| contents | The diadic $C^*$-algebra $\cQ_2$ contains canonically a copy of the Cuntz algebra $\cO_2$. It is shown that the inclusion $\cO_2 \subset \cQ_2$ is $C^*$-irreducible and rigid. It follows that the injective envelopes of these two $C^*$-algebras are $*$-isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the inclusion $\cO_2 \subset \cQ_2$ Bassi, Jacopo Conti, Roberto Operator Algebras (MSC 2010) Primary: 46L05, Secondary: 47L40 The diadic $C^*$-algebra $\cQ_2$ contains canonically a copy of the Cuntz algebra $\cO_2$. It is shown that the inclusion $\cO_2 \subset \cQ_2$ is $C^*$-irreducible and rigid. It follows that the injective envelopes of these two $C^*$-algebras are $*$-isomorphic. |
| title | On the inclusion $\cO_2 \subset \cQ_2$ |
| topic | Operator Algebras (MSC 2010) Primary: 46L05, Secondary: 47L40 |
| url | https://arxiv.org/abs/2505.16759 |