A cocycle in the adjoint representation of the orthogonal free quantum groups
Operator Algebras
2016-12-06 v3
Abstract
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 II_1-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.
Keywords
Cite
@article{arxiv.1402.4798,
title = {A cocycle in the adjoint representation of the orthogonal free quantum groups},
author = {Pierre Fima and Roland Vergnioux},
journal= {arXiv preprint arXiv:1402.4798},
year = {2016}
}
Comments
18 pages ; v3 corrects a technical mistake in the proof of Lemma 3.9