On the zeroth L²-homology of a quantum group

We prove that the zeroth L²-Betti number of a compact quantum group vanishes unless the underlying C*-algebra is finite dimensional and that the zeroth L²-homology itself is nontrivial exactly when the quantum group is coamenable.

Verfasser: Kyed, David
Dokumenttypen:Artikel
Medientypen:Text
Erscheinungsdatum:2011
Publikation in MIAMI:14.11.2011
Datum der letzten Änderung:20.03.2023
Quelle:Münster Journal of Mathematics, 4 (2011), S. 119-128
Angaben zur Ausgabe:[Electronic ed.]
Fachgebiet (DDC):510: Mathematik
Lizenz:InC 1.0
Sprache:English
Format:PDF-Dokument
URN:urn:nbn:de:hbz:6-32449562328
Permalink:https://nbn-resolving.de/urn:nbn:de:hbz:6-32449562328
Onlinezugriff:mjm_vol_4_07.pdf

We prove that the zeroth L²-Betti number of a compact quantum group vanishes unless the underlying C*-algebra is finite dimensional and that the zeroth L²-homology itself is nontrivial exactly when the quantum group is coamenable.