The approximation property for locally compact quantum groups
The approximation property for locally compact quantum groups
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DOI：
10.1016/j.aim.2023.109452
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发表时间：
2023-05
影响因子：
1.7
通讯作者：
Matthew Daws;Jacek Krajczok;Christian Voigt
中科院分区：
文献类型：
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作者：
Matthew Daws;Jacek Krajczok;Christian Voigt
摘要研究了局部紧量子群的Haagerup-Kraus逼近性质，推广和统一了Kraus-Ruan和Crann的工作。在此过程中，我们讨论了量子群的乘子如何与局部紧量子群的C⁎代数理论相互作用。在这一背景下建立了逼近性质的几个继承性质，包括到量子子群的通路、离散量子群的自由积和双交叉积的对偶。我们还讨论了与弱⁎算子逼近性质的一个关系。对于离散量子群，我们在Arano-de⁎-Wahl工作的基础上，引入了逼近性质的一个中心变量，并将其与刚性C-Laat-张量范畴的逼近性质的一个版本联系起来。
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 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.