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Quantum spaces without group structure. (English) Zbl 1194.46109

Summary: We prove that some well known compact quantum spaces such as quantum tori and some quantum two-spheres do not admit a compact quantum group structure. This is achieved by considering existence of traces, characters and nuclearity of the corresponding \( \text{C}^*\)-algebras.

MSC:

46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
46L85 Noncommutative topology
17B37 Quantum groups (quantized enveloping algebras) and related deformations
81R60 Noncommutative geometry in quantum theory
20G42 Quantum groups (quantized function algebras) and their representations
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