We prove that discrete compact quantum groups (or more generally locally compact, under additional hypotheses) with coamenable dual are continuous fields over their central closed quantum subgroups, and the same holds for free products of discrete quantum groups with coamenable dual amalgamated over a common central subgroup. Along the way we also show that free products of continuous fields of C∗-algebras are again free via a Fell-topology characterization for C∗-field continuity, recovering a result of Blanchard’s in a somewhat more general setting.

中文翻译：

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局部紧致量子群的场：连续性和推出

我们证明了具有可收敛对偶的离散紧致量子群（或更一般地局部紧致，在附加假设下）是在它们的中心封闭量子子群上的连续场，同样适用于具有可收敛对偶的离散量子群在公共中心上合并的自由乘积子群。一路上，我们还展示了连续领域的免费产品C*-代数通过 Fell 拓扑表征再次自由C*- 场连续性，在更一般的环境中恢复了布兰查德的结果。