{"paper":{"title":"Strong rigidity of II$_1$ factors arising from malleable actions of w-rigid groups, II","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Sorin Popa","submitted_at":"2004-07-07T13:24:34Z","abstract_excerpt":"We prove that any isomorphism $\\theta:M_0\\simeq M$ of group measure space II$_1$ factors, $M_0=L^\\infty(X_0, \\mu_0) \\rtimes_{\\sigma_0} G_0$, $M=L^\\infty(X, \\mu) \\rtimes_{\\sigma} G$, with $G_0$ containing infinite normal subgroups with the relative property (T) of Kazhdan-Margulis (i.e. $G_0$ {\\it w-rigid}) and $G$ an ICC group acting by Bernoulli shifts $\\sigma$, essentially comes from an isomorphism of probability spaces which conjugates the actions. Moreover, any isomorphism $\\theta$ of $M_0$ onto a ``corner'' $pMp$ of $M$, for $p\\in M$ an idempotent, forces $p=1$. In particular, all group m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0407103","kind":"arxiv","version":10},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0407103/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}