{"paper":{"title":"Weyl groups and rigidity of von Neumann algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Adrian Ioana, Cyril Houdayer","submitted_at":"2025-08-11T17:13:09Z","abstract_excerpt":"Let $G$ be a noncompact semisimple algebraic group with trivial center, $S < G$ a maximal split torus, $H < G$ the centralizer of $S$ in $G$ and $\\Gamma < G$ an irreducible lattice. Consider the group measure space von Neumann algebra $\\mathscr M = \\operatorname{L}(\\Gamma \\curvearrowright G/H)$ associated with the nonsingular action $\\Gamma \\curvearrowright G/H$ and regard the group von Neumann algebra $M = \\operatorname{L}(\\Gamma)$ as a von Neumann subalgebra $M \\subset \\mathscr M$. We show that the group $\\operatorname{Aut}_M(\\mathscr M)$ of all unital normal $\\ast$-automorphisms of $\\mathsc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08194","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.08194/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"}