Dr. Roland Vergnioux | Free entropy dimension and the orthogonal free quantum groups

Описание: Speaker: Dr Roland Vergnioux (Université de Caen Basse-Normandie)
Date: 4th May 2017 - 14:00 to 15:00
Venue: INI Seminar Room 2
Title: Free entropy dimension and the orthogonal free quantum groups
Event: (OAS) Operator algebras: subfactors and their applications
Abstract: 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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