Examples of weakly amenable discrete quantum groups

By Amaury Freslon. 2012

59 citations recorded by the source corpus.

We prove that Wang's free orthogonal and free unitary quantum groups are weakly amenable and that their Cowling-Haagerup constant is equal to 1. This is achieved by estimating the completely bounded norm of the projections on the coefficients of irreducible representations of their compact duals. An argument of monoidal equivalence then allows us to extend this result to quantum automorphism groups of finite spaces and even yields some examples of weakly amenable non-unimodular discrete quantum groups with the Haagerup property.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/78fe9283093f6e6ba39d41e8a9c3f4a1ddcde7c1

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Citations in the corpus

Reduced operator algebras of trace-preserving quantum automorphism groups (2012, background): “Based on recent work of Freslon [22] on the weak amenability free orthogonal quantum groups, we expect that L∞(G) always has this approximation property.”
Examples of factors which have no Cartan subalgebras (2012, unknown): “Then optimal constants [13].”
On the classification of easy quantum groups (2012, background): “e others in a couple of papers (see for instance [BS09], [BCS10], [BCS11], [BBC07]). Further operator algebraic aspects of some of the easy quantum groups have been studied in [VV07], [B12a], [B12b], [F12]. The link between easy quantum groups and free probability theory has been discovered by Ko¨st”
The Haagerup property for locally compact quantum groups (2013, background): “The main result of [36] has very recently been extended in [26], by other techniques, to duals of all free orthogonal quantum groups.”
The Connes embedding property for quantum group von Neumann algebras (2014, background): “These connections occur at the lev l of quantum symmetries and asymptotic freeness results [3, 6, 10, 17, 18], and also at th e operator algebra level [9, 19, 21, 22, 23, 35].”
CCAP for Universal Discrete Quantum Groups (2013, methodology): “Using a precursory idea of this paper, the second author showed the CCAP of FOF when O + F is monoidally equivalent to a Kac one Om [19].”