{"paper":{"title":"Compressible subalgebras in II$_1$ factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Sorin Popa","submitted_at":"2025-10-20T01:06:58Z","abstract_excerpt":"Given a II$_1$ factor $M$, a W$^*$-subalgebra $Q\\subset M$ is {\\it compressible} if for any $\\varepsilon>0$ there exists a finite set of unitary elements $\\Cal U_0\\subset \\Cal U(M)$ such that $\\| \\frac{1}{|\\Cal U_0|}\\sum_{u\\in \\Cal U_0} uxu^* -E_{1\\otimes \\Bbb M_K(\\Bbb C)}(x)\\|\\leq \\varepsilon$, $\\forall K\\geq 1$, $\\forall x\\in (Q\\otimes \\Bbb M_K(\\Bbb C))_1$. Any W$^*$-subalgebra $Q$ in a II$_1$ factor $M$ which admits a diffuse W$^*$-algebra $Q_0\\subset M$ that's free independent to $Q$, is compressible in $M$. We prove that if $Q\\subset M$ is compressible, then $_NL^2M_Q$ contains a copy of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.17076","kind":"arxiv","version":2},"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/2510.17076/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"}