Symmetry of some noncommutative sphere algebras
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912902985809920 |
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| author | Ugalde, William J. Várilly, Joseph C. |
| author_facet | Ugalde, William J. Várilly, Joseph C. |
| contents | Two known $q$-deformed (or `quantum') $7$-spheres, both denoted $\mathbb{S}^7_q$ in the literature, may be distinguished by the presence or absence of symmetry under $\mathrm{SU}_q(2)$. The quaternionic version of $\mathbb{S}^7_q$ has been shown by Brain and Landi to support such a symmetry. Here we show that this is not the case for the older $\mathbb{S}^7_q$ introduced by Vaksman and Soibelman: and as a consequence, these quantum $7$-spheres are not isomorphic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_06946 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry of some noncommutative sphere algebras Ugalde, William J. Várilly, Joseph C. Quantum Algebra 16T05 Two known $q$-deformed (or `quantum') $7$-spheres, both denoted $\mathbb{S}^7_q$ in the literature, may be distinguished by the presence or absence of symmetry under $\mathrm{SU}_q(2)$. The quaternionic version of $\mathbb{S}^7_q$ has been shown by Brain and Landi to support such a symmetry. Here we show that this is not the case for the older $\mathbb{S}^7_q$ introduced by Vaksman and Soibelman: and as a consequence, these quantum $7$-spheres are not isomorphic. |
| title | Symmetry of some noncommutative sphere algebras |
| topic | Quantum Algebra 16T05 |
| url | https://arxiv.org/abs/2602.06946 |