{"paper":{"title":"$L_p$-Representations of Discrete Quantum Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Michael Brannan, Zhong-Jin Ruan","submitted_at":"2014-04-16T04:03:50Z","abstract_excerpt":"Given a locally compact quantum group $\\mathbb G$, we define and study representations and C$^\\ast$-completions of the convolution algebra $L_1(\\mathbb G)$ associated with various linear subspaces of the multiplier algebra $C_b(\\mathbb G)$. For discrete quantum groups $\\mathbb G$, we investigate the left regular representation, amenability and the Haagerup property in this framework. When $\\mathbb G$ is unimodular and discrete, we study in detail the C$^\\ast$-completions of $L_1(\\mathbb G)$ associated with the non-commutative $L_p$-spaces $L_p(\\mathbb G)$. As an application of this theory, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4133","kind":"arxiv","version":3},"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"}