{"paper":{"title":"Noncommutative topological boundaries and amenable invariant random intermediate subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Shuoxing Zhou","submitted_at":"2024-07-15T16:59:18Z","abstract_excerpt":"As an analogue of the topological boundary of discrete groups $\\Gamma$, we define the noncommutative topological boundary of tracial von Neumann algebras $(M, \\tau)$ and apply it to generalize the main results of [AHO23], showing that for a trace-preserving action $\\Gamma \\curvearrowright (A, \\tau_A)$ on an amenable tracial von Neumann algebra, any $\\Gamma$-invariant amenable intermediate subalgebra between $A$ and $\\Gamma \\ltimes A$ is necessarily a subalgebra of $\\mathrm{Rad}(\\Gamma) \\ltimes A$. By taking $(A, \\tau_A) = L^\\infty(X, \\nu_X)$ for a free pmp action $\\Gamma \\curvearrowright (X, \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.10905","kind":"arxiv","version":4},"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/2407.10905/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"}