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Amenability and Co-Amenability for Locally Compact Quantum Groups

E. Bédos

Institute of Mathematics, University of Oslo, P.B. 1053 Blindern, 0316 Oslo, Norway

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and

L. Tuset

Faculty of Engineering, Oslo University College, Cort Adelers Gate 30, 0254 Oslo, Norway

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https://doi.org/10.1142/S0129167X03002046Cited by:64 (Source: Crossref)

Abstract

We define concepts of amenability and co-amenability for locally compact quantum groups in the sense of J. Kustermans and S. Vaes. Co-amenability of a lcqg (locally compact quantum group) is proved to be equivalent to a series of statements, all of which imply amenability of the dual lcqg. Further, it is shown that if a lcqg is amenable, then its universal dual lcqg is nuclear. We also define and study amenability and weak containment concepts for representations and corepresentations of lcqg's.

Keywords:

AMSC: 22D10, 22D25, 43A07, 43A65, 46L05, 46L55

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