The approximation property for locally compact quantum groups

Daws, M., Krajczok, J. and Voigt, C. (2024) The approximation property for locally compact quantum groups. Advances in Mathematics, 438, 109452. (doi: 10.1016/j.aim.2023.109452)

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We study the Haagerup–Kraus approximation property for locally compact quantum groups, generalising and unifying previous work by Kraus–Ruan and Crann. Along the way we discuss how multipliers of quantum groups interact with the C∗-algebraic theory of locally compact quantum groups. Several inheritance properties of the approximation property are established in this setting, including passage to quantum subgroups, free products of discrete quantum groups, and duals of double crossed products. We also discuss a relation to the weak∗ operator approximation property. For discrete quantum groups, we introduce a central variant of the approximation property, and relate this to a version of the approximation property for rigid C∗-tensor categories, building on work of Arano–De Laat–Wahl.

Item Type:Articles
Additional Information:This work was supported by EPSRC grants EP/T03064X/1 and EP/T030992/1.
Keywords:Locally compact quantum groups, approximation property.
Glasgow Author(s) Enlighten ID:Krajczok, Dr Jacek and Voigt, Professor Christian
Authors: Daws, M., Krajczok, J., and Voigt, C.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
ISSN (Online):1090-2082
Published Online:02 January 2024
Copyright Holders:Copyright © 2023 The Author(s)
First Published:First published in Advances in Mathematics 438:109452
Publisher Policy:Reproduced under a Creative Commons license
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
309470Quantum groups in actionChristian VoigtEngineering and Physical Sciences Research Council (EPSRC)EP/T03064X/1M&S - Mathematics