Approximation properties for free orthogonal and free unitary quantum groups

Details Approximation properties for free orthogonal and free unitary quantum groups Approximation properties for free orthogonal and free unitary quantum groups

2011-03-01

arxiv.org/abs/1103.0264v2

Mathematics

Operator Algebras

Minor corrections

Scientific paper

We show that the reduced von Neumann algebras of the free orthogonal and free unitary quantum groups have the Haagerup approximation property. Using this result and a Haagerup-type inequality for these quantum groups due to Vergnioux (J. Operator Theory 57, 303-324 (2007)), we also show that the reduced C$^\ast$-algebras of the free orthogonal and free unitary quantum groups have the metric approximation property.

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