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Property $T$ for general locally compact quantum groups
- Publication Year :
- 2015
-
Abstract
- In this short article, we obtained some equivalent formulations of property $T$ for a general locally compact quantum group $\mathbb{G}$, in terms of the full quantum group $C^*$-algebras $C_0^\mathrm{u}(\widehat{\mathbb{G}})$ and the $*$-representation of $C_0^\mathrm{u}(\widehat{\mathbb{G}})$ associated with the trivial unitary corepresentation (that generalize the corresponding results for locally compact groups). Moreover, if $\mathbb{G}$ is of Kac type, we show that $\mathbb{G}$ has property $T$ if and only if every finite dimensional irreducible $*$-representation of $C_0^\mathrm{u}(\widehat{\mathbb{G}})$ is an isolated point in the spectrum of $C_0^\mathrm{u}(\widehat{\mathbb{G}})$ (this also generalizes the corresponding locally compact group result). In addition, we give a way to construct property $T$ discrete quantum groups using bicrossed products.<br />Comment: 12 pages; accepted for publication in Int. J. Math
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1509.02262
- Document Type :
- Working Paper