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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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