The Haagerup property for locally compact quantum groups
By Matthew Daws, Pierre Fima, Adam G. Skalski, Stuart White. 2013
84 citations recorded by the source corpus.
The Haagerup property for locally compact groups is generalised to the context of locally compact quantum groups, with several equivalent characterisations in terms of the unitary representations and positive-definite functions established. In particular it is shown that a locally compact quantum group G has the Haagerup property if and only if its mixing representations are dense in the space of all unitary representations. For discrete G we characterise the Haagerup property by the existence of a symmetric proper conditionally negative functional on the dual quantum group $\hat{G}$; by the existence of a real proper cocycle on G, and further, if G is also unimodular we show that the Haagerup property is a von Neumann property of G. This extends results of Akemann, Walter, Bekka, Cherix, Valette, and Jolissaint to the quantum setting and provides a connection to the recent work of Brannan. We use these characterisations to show that the Haagerup property is preserved under free products of discrete quantum groups.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8e82bbaaebf89534870328716f77a5a99958ea71
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Citations in the corpus
- Easy quantum groups and quantum subgroups of a semi-direct product quantum group (2013, background): “Recently, in [DFSW13] the notion was systematically investigated in the framework of quantum groups.”
- Operator Algebras in Rigid C*-Tensor Categories (2016, unknown): “n-standard. For a general overview of analytic properties (and many equivalent characterizations of the above properties) for locally compact quantum groups in general, we recommend the survey papers [DFSW16] and [DSV16], and the references therein. Our denitions can be seen to be equivalent to the ”