International Journal of Mathematics and Mathematical Sciences
Volume 31 (2002), Issue 10, Pages 577-601
doi:10.1155/S016117120210603X
Amenability and coamenability of algebraic quantum groups
Erik Bédos1
, Gerard J. Murphy2
and Lars Tuset3
1Institute of Mathematics, University of Oslo, P.B. 1053 Blindern, Oslo 0316, Norway
2Department of Mathematics, National University of Ireland, Cork, Ireland
3Faculty of Engineering, Oslo University College, Cort Adelers Gate 30, Oslo 0254, Norway
Abstract
We define concepts of amenability and coamenability for algebraic quantum groups in the sense of Van Daele (1998). We show that coamenability of an algebraic quantum group always implies amenability of its dual. Various necessary and/or sufficient conditions for amenability or coamenability are obtained. Coamenability is shown to have interesting consequences for the modular theory in the case that the algebraic quantum group is of compact type.