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Approximation properties for locally compact quantum groups

Volume 111 / 2017

Michael Brannan Banach Center Publications 111 (2017), 185-232 MSC: 46L65, 46L54, 20G42, 20F65. DOI: 10.4064/bc111-0-6


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.


  • Michael BrannanDepartment of Mathematics
    Texas A&M University
    Mailstop 3368
    College Station
    TX 77843-3368, USA

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