Amenability and the bicrossed product construction

By P. deSmedt, J. Quaegebeur, S. Vaes. 2001

48 citations recorded by the source corpus.

We study stability properties of amenable locally compact quantum groups under the bicrossed product construction. We obtain as our main result an equivalence between amenability of the bicrossed product and amenability of the matched quantum groups used as building ingredients of the bicrossed product. Finally, we give examples of non-amenable locally compact quantum groups obtained by a bicrossed product construction.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/54006fc8d5eff10ca505b2aac2c32a6421607e21

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Non-Semi-Regular Quantum Groups Coming from Number Theory (2002, background): “ed strong Morita equivalence. b) Because of the Morita equivalence above, the projection of S⋊ f Sˆ onto S⋊ r Sˆ is faithful if and only if the projection of S u onto Sis faithful. From Theorem 15 in [6], it follows that this last projection is faithful if and only if G 2 is amenable. Because of con”
Amenable discrete quantum groups (2003, background): “ a ﬁnite dimensional representation. (4) The C∗-algebra Aˆ is nuclear. (5) The von Neumann algebra Mˆ is injective. Amenability of quantum groups are studied in [B-M-T1], [B-M-T2], [B-M-T3], [B-C-T], [D-Q-V], for example. We emphasize that our main theorem is more general than their versions of Z.-J”
Strictly Outer Actions of Groups and Quantum Groups (2002, background): “A l.c. quantum group has a left invariant mean if and only if it has an invariant mean, see e.g. Proposition 3 in [ 9 ].”