{"paper":{"title":"Non-commutative Intermediate Factor theorem associated with $W^*$-dynamics of product groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.FA","math.GN"],"primary_cat":"math.OA","authors_text":"Shuoxing Zhou, Tattwamasi Amrutam, Yongle Jiang","submitted_at":"2025-08-26T12:25:49Z","abstract_excerpt":"Let $G = G_{1} \\times G_{2}$ be a product of two locally compact, second countable groups and $\\mu \\in \\mathrm{Prob}(G)$ be of the form $\\mu = \\mu_{1} \\times \\mu_{2}$, where $\\mu_{i} \\in \\mathrm{Prob}(G_{i})$. Let $(B,\\nu_B)$ be the associated Poisson boundary. We show that every intermediate $G$-von Neumann algebra $\\mathcal{M}$ with \\[ \\mathcal{N} \\subseteq \\mathcal{M} \\subseteq \\mathcal{N} \\,\\bar{\\otimes}\\, L^{\\infty}(B,\\nu) \\] splits as a tensor product of the form $\\mathcal{N}\\bar{\\otimes}L^{\\infty}(C,\\nu_C)$, where $(C,\\nu_C)$ is a $(G,\\mu)$-boundary. Here, $\\mathcal{N}$ is a tracial von"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.18978","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.18978/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"}