Amenability and the bicrossed product construction. (English) Zbl 1035.46042

Desmedt, Pieter; Quaegebeur, Johan; Vaes, Stefaan

Ill. J. Math. 46, No. 4, 1259-1277 (2002).

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.

Reviewer: Tomasz Brzeziński (Swansea)

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