Orthogonal free quantum group factors are strongly 1-bounded

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.

v3: accepted version

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Cited by in corpus (4)

• Noncommutative Furstenberg boundary
• On MASAs in $q$-deformed von Neumann algebras
• Second cohomology groups of the Hopf${}^{\ast }$-algebras associated to universal unitary quantum groups
• Strong 1-Boundedness of Unimodular Free Orthogonal Quantum Groups