The approximation property for locally compact quantum groups

Daws, Matthew and Krajczok, Jacek and Voigt, Christian (2024) The approximation property for locally compact quantum groups. Advances in Mathematics, 438: 109452. ISSN 0001-8708

[thumbnail of 2305.04894]
Text (2305.04894) - Accepted Version
Available under License Creative Commons Attribution.

Download (0B)
[thumbnail of 2305.04894]
Text (2305.04894) - Accepted Version
Available under License Creative Commons Attribution.

Download (0B)
[thumbnail of 2305.04894]
Text (2305.04894)
2305.04894.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (769kB)

Abstract

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 $\mathrm{C}^*$-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 $\mathrm{C}^*$-tensor categories, building on work of Arano--De Laat--Wahl.

Item Type:
Journal Article
Journal or Publication Title:
Advances in Mathematics
Uncontrolled Keywords:
Research Output Funding/yes_externally_funded
Subjects:
?? locally compact quantum groupsapproximation propertyyes - externally fundedyesgeneral mathematics ??
ID Code:
210630
Deposited By:
Deposited On:
28 Nov 2023 14:50
Refereed?:
Yes
Published?:
Published
Last Modified:
16 Jul 2024 00:36