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arXiv · 2411.11043

An analytic characterization of freeness for finitely generated discrete quantum groups

Yoonje Jeong·Sang-Gyun Youn
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Abstract

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.

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Yoonje Jeong, Sang-Gyun Youn. 2024-11-17. An analytic characterization of freeness for finitely generated discrete quantum groups. https://arxiv.org/abs/2411.11043

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