Annals of Functional Analysis
- Ann. Funct. Anal.
- Volume 9, Number 2 (2018), 210-219.
Bekka-type amenabilities for unitary corepresentations of locally compact quantum groups
In this short note, we further Ng’s work by extending Bekka amenability and weak Bekka amenability to general locally compact quantum groups, and we generalize some of Ng’s results to the general case. In particular, we show that a locally compact quantum group is coamenable if and only if the contra-corepresentation of its fundamental multiplicative unitary is Bekka-amenable, and that is amenable if and only if its dual quantum group’s fundamental multiplicative unitary is weakly Bekka-amenable.
Ann. Funct. Anal., Volume 9, Number 2 (2018), 210-219.
Received: 23 January 2017
Accepted: 5 May 2017
First available in Project Euclid: 7 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 20G42: Quantum groups (quantized function algebras) and their representations [See also 16T20, 17B37, 81R50]
Secondary: 46L89: Other "noncommutative" mathematics based on C-algebra theory [See also 58B32, 58B34, 58J22] 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx]
Chen, Xiao. Bekka-type amenabilities for unitary corepresentations of locally compact quantum groups. Ann. Funct. Anal. 9 (2018), no. 2, 210--219. doi:10.1215/20088752-2017-0044. https://projecteuclid.org/euclid.afa/1512637230