Quantum hypergroups arising from ergodic coactions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911664551493632 |
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| author | De Ro, Joeri |
| author_facet | De Ro, Joeri |
| contents | Given a locally compact quantum group $\mathbb{G}$ and an ergodic, integrable action $L^\infty(\mathbb{X})\stackrelα\curvearrowleft \mathbb{G}$, the von Neumann algebra $L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}}):= L^\infty(\mathbb{X})\square \overline{L^\infty(\mathbb{X})}$ is shown to carry a natural normal ucp coassociative map $Δ_{\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}}}: L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}})\to L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}})\bar{\otimes} L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}})$. Restricting to the class of compact quantum groups, this provides a large class of new examples of (analytical) compact quantum hypergroups. We provide characterizations of coamenability for these compact quantum hypergroups, making use of the theory of equivariant correspondences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_08459 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum hypergroups arising from ergodic coactions De Ro, Joeri Operator Algebras Quantum Algebra Given a locally compact quantum group $\mathbb{G}$ and an ergodic, integrable action $L^\infty(\mathbb{X})\stackrelα\curvearrowleft \mathbb{G}$, the von Neumann algebra $L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}}):= L^\infty(\mathbb{X})\square \overline{L^\infty(\mathbb{X})}$ is shown to carry a natural normal ucp coassociative map $Δ_{\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}}}: L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}})\to L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}})\bar{\otimes} L^\infty(\mathbb{X}\times_{\mathbb{G}}\bar{\mathbb{X}})$. Restricting to the class of compact quantum groups, this provides a large class of new examples of (analytical) compact quantum hypergroups. We provide characterizations of coamenability for these compact quantum hypergroups, making use of the theory of equivariant correspondences. |
| title | Quantum hypergroups arising from ergodic coactions |
| topic | Operator Algebras Quantum Algebra |
| url | https://arxiv.org/abs/2605.08459 |