{"paper":{"title":"Property $T$ for general locally compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OA"],"primary_cat":"math.QA","authors_text":"Chi-Keung Ng, Xiao Chen","submitted_at":"2015-09-08T06:55:23Z","abstract_excerpt":"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}(\\wid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02262","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}