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Fields of locally compact quantum groups: Continuity and pushouts

Department of Mathematics, University at Buffalo, Buffalo, NY 14260-2900, USA

https://doi.org/10.1142/S0129167X21500646Cited by:0 (Source: Crossref)

Abstract

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 $C^{*}$ $C^{*}$ -algebras are again free via a Fell-topology characterization for $C^{*}$ $C^{*}$ -field continuity, recovering a result of Blanchard’s in a somewhat more general setting.

Communicated by Yasuyuki Kawahigashi

Keywords:

AMSC: 46L09, 20G42, 18A30, 46L65

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