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Article Dans Une Revue International Mathematics Research Notices Année : 2015

A cocycle in the adjoint representation of the orthogonal free quantum groups

Pierre Fima
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Résumé

We show that the orthogonal free quantum groups are not inner amenable and we construct an explicit proper cocycle weakly contained in the regular representation. This strengthens the result of Vaes and the second author, showing that the associated von Neumann algebras are full II1-factors and Brannan's result showing that the orthogonal free quantum groups have Haagerup's approximation property. We also deduce Ozawa–Popa's property strong (HH) and give a new proof of Isono's result about strong solidity.

Dates et versions

hal-01277198 , version 1 (22-02-2016)

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Pierre Fima, Roland Vergnioux. A cocycle in the adjoint representation of the orthogonal free quantum groups. International Mathematics Research Notices, 2015, 2015 (20), pp.10069-10094. ⟨10.1093/imrn/rnu268⟩. ⟨hal-01277198⟩
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