{"paper":{"title":"Quantum Isometry group of dual of finitely generated discrete groups and quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Arnab Mandal, Debashish Goswami","submitted_at":"2014-08-25T08:55:43Z","abstract_excerpt":"We study quantum isometry groups, denoted by $\\mathbb{Q}(\\Gamma, S)$, of spectral triples on $C^*_r(\\Gamma)$ for a finitely generated discrete group coming from the word-length metric with respect to a symmetric generating set $S$. We first prove a few general results about $\\mathbb{Q}(\\Gamma, S)$ including : \\begin{itemize} \\item For a group $\\Gamma$ with polynomial growth property, the dual of $\\mathbb{Q}(\\Gamma, S)$ has polynomial growth property provided the action of $\\mathbb{Q}(\\Gamma,S)$ on $C^*_r(\\Gamma)$ has full spectrum, \\item $\\mathbb{Q}(\\Gamma, S) \\cong QISO(\\hat{\\Gamma}, d)$ for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5683","kind":"arxiv","version":4},"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"}