{"paper":{"title":"Completely bounded representations of convolution algebras of locally compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Ebrahim Samei, Matthew Daws, Michael Brannan","submitted_at":"2011-07-11T19:08:15Z","abstract_excerpt":"Given a locally compact quantum group $\\mathbb G$, we study the structure of completely bounded homomorphisms $\\pi:L^1(\\mathbb G)\\rightarrow\\mathcal B(H)$, and the question of when they are similar to $\\ast$-homomorphisms. By analogy with the cocommutative case (representations of the Fourier algebra $A(G)$), we are led to consider the associated map $\\pi^*:L^1_\\sharp(\\mathbb G) \\rightarrow \\mathcal B(H)$ given by $\\pi^*(\\omega) = \\pi(\\omega^\\sharp)^*$. We show that the corepresentation $V_\\pi$ of $L^\\infty(\\mathbb G)$ associated to $\\pi$ is invertible if and only if both $\\pi$ and $\\pi^*$ are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2094","kind":"arxiv","version":2},"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"}