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\(K\)-amenability for amalgamated free products of amenable discrete quantum groups.(English)Zbl 1064.46064

Summary: The basic notions and results of equivariant KK-theory concerning crossed products can be extended to the case of locally compact quantum groups. We recall these constructions and prove some useful properties of subgroups and amalgamated free products of discrete quantum groups. Using these properties and a quantum analogue of the Bass-Serre tree, we establish the K-amenability of amalgamated free products of amenable discrete quantum groups.

MSC:

46L80 \(K\)-theory and operator algebras (including cyclic theory)
19K35 Kasparov theory (\(KK\)-theory)
20G42 Quantum groups (quantized function algebras) and their representations
58B32 Geometry of quantum groups

Cite

References:

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This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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