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arXiv · 1703.08134

Orthogonal free quantum group factors are strongly 1-bounded

Michael Brannan·Roland Vergnioux
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Abstract

We prove that the orthogonal free quantum group factors $\mathcal{L}(\mathbb{F}O_N)$ are strongly $1$-bounded in the sense of Jung. In particular, they are not isomorphic to free group factors. This result is obtained by establishing a spectral regularity result for the edge reversing operator on the quantum Cayley tree associated to $\mathbb{F}O_N$, and combining this result with a recent free entropy dimension rank theorem of Jung and Shlyakhtenko.

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Michael Brannan, Roland Vergnioux. 2017-03-23. Orthogonal free quantum group factors are strongly 1-bounded. https://doi.org/10.1016/j.aim.2018.02.007

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