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Amenability and the bicrossed product construction. (English) Zbl 1035.46042
The main aim of this paper is to establish when a bicrossproduct of locally compact quantum groups is an amenable quantum group. It is shown that a (cocycle) bicrossproduct is (weakly) amenable if and only if each of the locally compact quantum groups on which the (cocycle) bicrossproduct quantum group is built is (weakly) amenable. The authors also use the bicrossproduct construction to give examples of non-amenable locally compact quantum groups.

##### MSC:
 46L89 Other “noncommutative” mathematics based on $$C^*$$-algebra theory 43A07 Means on groups, semigroups, etc.; amenable groups 46L65 Quantizations, deformations for selfadjoint operator algebras
##### Keywords:
locally compact quantum group; bicrossproduct; amenability
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