An analytic characterization of freeness for finitely generated discrete quantum groups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910816274481152 |
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| author | Jeong, Yoonje Youn, Sang-Gyun |
| author_facet | Jeong, Yoonje Youn, Sang-Gyun |
| contents | We prove that a freer quantum group has smaller moments of the self-adjoint main character in the category of finitely generated discrete quantum groups. As a result, the moments are minimized precisely by the unitary free quantum groups $\mathbb{F}U(Q)$. Furthermore, in the spirit of [CC22], we prove that the operator norm of the self-adjoint main character is minimized only by unitary free quantum groups, at least in the subcategory of duals of free quantum groups of Kac type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11043 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An analytic characterization of freeness for finitely generated discrete quantum groups Jeong, Yoonje Youn, Sang-Gyun Quantum Algebra Functional Analysis Operator Algebras 46L67, 20G42, 46L54 We prove that a freer quantum group has smaller moments of the self-adjoint main character in the category of finitely generated discrete quantum groups. As a result, the moments are minimized precisely by the unitary free quantum groups $\mathbb{F}U(Q)$. Furthermore, in the spirit of [CC22], we prove that the operator norm of the self-adjoint main character is minimized only by unitary free quantum groups, at least in the subcategory of duals of free quantum groups of Kac type. |
| title | An analytic characterization of freeness for finitely generated discrete quantum groups |
| topic | Quantum Algebra Functional Analysis Operator Algebras 46L67, 20G42, 46L54 |
| url | https://arxiv.org/abs/2411.11043 |