{"paper":{"title":"Quasi-regular representations of discrete groups and associated C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Bachir Bekka, Mehrdad Kalantar","submitted_at":"2019-03-01T08:42:46Z","abstract_excerpt":"Let $G$ be a countable group. We introduce several equivalence relations on the set ${\\rm Sub}(G)$ of subgroups of $G$, defined by properties of the quasi-regular representations $\\lambda_{G/H}$ associated to $H\\in {\\rm Sub}(G)$ and compare them to the relation of $G$-conjugacy of subgroups. We define a class ${\\rm Sub}_{\\rm sg}(G)$ of subgroups (these are subgroups with a certain spectral gap property) and show that they are rigid, in the sense that the equivalence class of $H\\in {\\rm Sub}_{\\rm sg}(G)$ for any one of the above equivalence relations coincides with the $G$-conjugacy class of $H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00202","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"}