On the geometry of quantum spheres and hyperboloids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917585971314688 |
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| author | Landi, Giovanni Pagani, Chiara |
| author_facet | Landi, Giovanni Pagani, Chiara |
| contents | We study two classes of quantum spheres and hyperboloids which are $*$-quantum spaces for the quantum orthogonal group $\mathcal{O}(SO_q(3))$. We construct line bundles over the quantum homogeneous space of invariant elements for the quantum subgroup $SO(2)$ of $SO_q(3)$. These are associated to the quantum principal bundle via corepresentations of $SO(2)$ and are given by finitely-generated projective modules $\mathcal{E}_n$ of rank $1$ and even degree $-2n$. The corresponding idempotents, representing classes in K-theory, are explicitly worked out. For $q$ real, we diagonalise the Casimir operator of the Hopf algebra ${\mathcal{U}_{q^{1/2}}(sl_2)}$ dual to $\mathcal{O}(SO_q(3))$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_06356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the geometry of quantum spheres and hyperboloids Landi, Giovanni Pagani, Chiara Quantum Algebra Mathematical Physics We study two classes of quantum spheres and hyperboloids which are $*$-quantum spaces for the quantum orthogonal group $\mathcal{O}(SO_q(3))$. We construct line bundles over the quantum homogeneous space of invariant elements for the quantum subgroup $SO(2)$ of $SO_q(3)$. These are associated to the quantum principal bundle via corepresentations of $SO(2)$ and are given by finitely-generated projective modules $\mathcal{E}_n$ of rank $1$ and even degree $-2n$. The corresponding idempotents, representing classes in K-theory, are explicitly worked out. For $q$ real, we diagonalise the Casimir operator of the Hopf algebra ${\mathcal{U}_{q^{1/2}}(sl_2)}$ dual to $\mathcal{O}(SO_q(3))$. |
| title | On the geometry of quantum spheres and hyperboloids |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2402.06356 |