Communications in Mathematical Physics

, Volume 331, Issue 3, pp 1041–1069 | Cite as

Weak Amenability of Locally Compact Quantum Groups and Approximation Properties of Extended Quantum SU(1, 1)

  • Martijn CaspersEmail author


We study weak amenability for locally compact quantum groups in the sense of Kustermans and Vaes. In particular, we focus on non-discrete examples. We prove that a coamenable quantum group is weakly amenable if there exists a net of positive, scaling invariant elements in the Fourier algebra \({A(\mathbb{G})}\) whose representing multipliers form an approximate identity in \({C_0(\mathbb{G})}\) that is bounded in the \({M0A(\mathbb{G})}\) norm; the bound being an upper estimate for the associated Cowling–Haagerup constant.

As an application, we find the appropriate approximation properties of the extended quantum SU(1, 1) group and its dual. That is, we prove that it is weakly amenable and coamenable. Furthermore, it has the Haagerup property in the quantum group sense, introduced by Daws, Fima, Skalski and White.


Quantum Group Approximate Identity Norm Core Compact Quantum Group Basic Hypergeometric Series 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Laboratoire de MathématiquesUniversité de Franche-ComtéBesançonFrance

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