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Compact operators in regular LCQ groups. (English) Zbl 1314.46083
Summary: We show that a regular locally compact quantum group $$\mathbb{G}$$ is discrete if and only if $$\mathcal{L}^{\infty}(\mathbb{G})$$ contains non-zero compact operators on $$\mathcal{L}^{2}(\mathbb{G})$$. As a corollary we classify all discrete quantum groups among regular locally compact quantum groups $$\mathbb{G}$$ where $$\mathcal{L}^{1}(\mathbb{G})$$ has the Radon-Nikodym property.
Reviewer: Reviewer (Berlin)

##### MSC:
 46L89 Other “noncommutative” mathematics based on $$C^*$$-algebra theory 46B22 Radon-Nikodým, Kreĭn-Milman and related properties 17B37 Quantum groups (quantized enveloping algebras) and related deformations
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