×

Approximation properties for locally compact quantum groups. (English) Zbl 1372.46053

Franz, Uwe (ed.) et al., Topological quantum groups. Lectures of the graduate school on topological quantum groups, Będlewo, Poland, June 28 – July 11, 2015. Warsaw: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-35-5/pbk). Banach Center Publications 111, 185-232 (2017).
Summary: This is a survey of some aspects of the subject of approximation properties for locally compact quantum groups, based on lectures given at the Topological Quantum Groups Graduate School, 28 June-11 July, 2015 in Będlewo, Poland. We begin with a study of the dual notions of amenability and co-amenability, and then consider weakenings of these properties in the form of the Haagerup property and weak amenability. For discrete quantum groups, the interaction between these properties and various operator algebra approximation properties are investigated. We also study the connection between central approximation properties for discrete quantum groups and monoidal equivalence for their compact duals. We finish by discussing the central weak amenability and central Haagerup property for free quantum groups.
For the entire collection see [Zbl 1364.46006].

MSC:

46L65 Quantizations, deformations for selfadjoint operator algebras
46L54 Free probability and free operator algebras
20G42 Quantum groups (quantized function algebras) and their representations
20F65 Geometric group theory
46-02 Research exposition (monographs, survey articles) pertaining to functional analysis
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] pp.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.