{"paper":{"title":"A class of II$_1$ factors with a unique McDuff decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.OA","authors_text":"Adrian Ioana, Pieter Spaas","submitted_at":"2018-08-08T23:42:49Z","abstract_excerpt":"We provide a fairly large class of II$_1$ factors $N$ such that $M=N\\bar{\\otimes}R$ has a unique McDuff decomposition, up to isomorphism, where $R$ denotes the hyperfinite II$_1$ factor. This class includes all II$_1$ factors $N=L^{\\infty}(X)\\rtimes\\Gamma$ associated to free ergodic probability measure preserving (p.m.p.) actions $\\Gamma\\curvearrowright (X,\\mu)$ such that either (a) $\\Gamma$ is a free group, $\\mathbb F_n$, for some $n\\geq 2$, or (b) $\\Gamma$ is a non-inner amenable group and the orbit equivalence relation of the action $\\Gamma\\curvearrowright (X,\\mu)$ satisfies a property intr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02965","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"}