{"paper":{"title":"Unique Cartan decomposition for II_1 factors arising from arbitrary actions of free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Sorin Popa, Stefaan Vaes","submitted_at":"2011-11-29T20:01:08Z","abstract_excerpt":"We prove that for any free ergodic probability measure preserving action \\F_n \\actson (X,\\mu) of a free group on n generators \\F_n, 2 \\leq n \\leq \\infty, the associated group measure space II_1 factor $L^\\infty(X) \\rtimes \\F_n$ has L^\\infty(X) as its unique Cartan subalgebra, up to unitary conjugacy. We deduce that group measure space II_1 factors arising from actions of free groups with different number of generators are never isomorphic. We actually prove unique Cartan decomposition results for II_1 factors arising from arbitrary actions of a rather large family of groups, including all free"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.6951","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"}