{"paper":{"title":"W*-superrigidity of mixing Gaussian actions of rigid groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"R\\'emi Boutonnet","submitted_at":"2012-09-27T13:41:32Z","abstract_excerpt":"We generalize W*-superrigidity results about Bernoulli actions of rigid groups to general mixing Gaussian actions. We thus obtain the following: If \\Gamma\\ is any ICC group which is w-rigid (i.e. it contains an infinite normal subgroup with the relative property (T)) then any mixing Gaussian action \\sigma\\ of \\Gamma\\ is W*-superrigid. More precisely, if \\rho\\ is another free ergodic action of a group \\Lambda\\ such that the crossed-product von Neumann algebras associated with \\rho\\ and \\sigma\\ are isomorphic, then \\Lambda\\ and \\Gamma\\ are isomorphic, and the actions \\rho\\ and \\sigma\\ are conjug"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6227","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"}