{"paper":{"title":"Maximal amenable MASAs of radial type in the free group factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Remi Boutonnet, Sorin Popa","submitted_at":"2023-02-26T17:11:13Z","abstract_excerpt":"We prove that if $\\{(M_j, \\tau_j)\\}_{j\\in J}$ are tracial von Neumann algebras, $s_j \\in M_j$ are selfadjoint semicircular elements and $t=(t_j)_j$ is a square summable $J$-tuple of real numbers with at least two non-zero entries, then the von Neumann algebra $A(t)$ generated by the ``weighted radial element'' $\\sum_j t_j s_j\\in M:=*_{j\\in J} M_j$ is maximal amenable in $M$, with $A(t)$, $A(t')$ unitary conjugate in $M$ iff $t, t'$ are proportional. Letting $M_j$ be diffuse amenable, $\\forall j$, this provides a large family of maximal amenable MASAs in the free group factor $L\\mathbb F_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.13355","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/2302.13355/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"}