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| Format: | Preprint |
| Published: |
2024
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| Online Access: | https://arxiv.org/abs/2406.17288 |
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| _version_ | 1866918092050792448 |
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| author | D'Andrea, Francesco |
| author_facet | D'Andrea, Francesco |
| contents | For $n\in\mathbb{N}$ and $q\in [0,1[$, the Vaksman-Soibelman quantum sphere $S^{2n+1}_q$ is described by an associative algebra $\mathcal{A}(S^{2n+1}_q)$ deforming the algebra of polynomial functions on the 2n+1 dimensional unit sphere. Its C*-enveloping algebra is known to be independent of the deformation parameter q. In contrast to what happens in the C*-algebraic setting, we show here that, for all $q,q'$ in the above range, $\mathcal{A}(S^{2n+1}_q)$ is isomorphic to $\mathcal{A}(S^{2n+1}_{q'})$ only if $q=q'$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17288 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Isomorphisms of quantum spheres D'Andrea, Francesco Quantum Algebra Primary: 16T20, Secondary: 20G42 For $n\in\mathbb{N}$ and $q\in [0,1[$, the Vaksman-Soibelman quantum sphere $S^{2n+1}_q$ is described by an associative algebra $\mathcal{A}(S^{2n+1}_q)$ deforming the algebra of polynomial functions on the 2n+1 dimensional unit sphere. Its C*-enveloping algebra is known to be independent of the deformation parameter q. In contrast to what happens in the C*-algebraic setting, we show here that, for all $q,q'$ in the above range, $\mathcal{A}(S^{2n+1}_q)$ is isomorphic to $\mathcal{A}(S^{2n+1}_{q'})$ only if $q=q'$. |
| title | Isomorphisms of quantum spheres |
| topic | Quantum Algebra Primary: 16T20, Secondary: 20G42 |
| url | https://arxiv.org/abs/2406.17288 |