Back to Search
Start Over
Amenability of locally compact quantum groups and their unitary co-representations
- Source :
- Bull. Lond. Math. Soc. 49 (2017), no. 3, 491-498
- Publication Year :
- 2016
-
Abstract
- We prove that amenability of a unitary co-representation $U$ of a locally compact quantum group passes to unitary co-representations that weakly contain $U$. This generalizes a result of Bekka, and answers affirmatively a question of B\'edos, Conti and Tuset. As a corollary, we extend to locally compact quantum groups a result of the first-named author, which characterizes amenability of a locally compact group $G$ by nuclearity of the reduced group $C^{*}$-algebra $C_{r}^{*}(G)$ and an additional condition.<br />Comment: 9 pages; a new co-author; added to Theorem 3.2 a second part about the case of a trivial scaling group, and gave an alternative proof of one of the implications; to appear in the Bulletin of the London Mathematical Society
Details
- Database :
- arXiv
- Journal :
- Bull. Lond. Math. Soc. 49 (2017), no. 3, 491-498
- Publication Type :
- Report
- Accession number :
- edsarx.1609.08920
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1112/blms.12047