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Free entropy dimension and the orthogonal free quantum groups

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OAS - Operator algebras: subfactors and their applications

Orthogonal free quantum groups have been extensively studied in the past two decades from the operator algebraic point of view, and were shown to share many analytical properties with the ordinary free groups. In a recent preprint with Michael Brannan, we prove that the associated von Neumann algebras 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 associated quantum Cayley tree, and combining this result with a recent free entropy dimension rank theorem of Jung and Shlyakhtenko.



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