{"paper":{"title":"Free independence in ultraproduct von Neumann algebras and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Cyril Houdayer, Yusuke Isono","submitted_at":"2014-08-25T12:39:36Z","abstract_excerpt":"The main result of this paper is a generalization of Popa's free independence result for subalgebras of ultraproduct ${\\rm II_1}$ factors [Po95] to the framework of ultraproduct von Neumann algebras $(M^\\omega, \\varphi^\\omega)$ where $(M, \\varphi)$ is a $\\sigma$-finite von Neumann algebra endowed with a faithful normal state satisfying $(M^\\varphi)' \\cap M = \\mathbf{C} 1$. More precisely, we show that whenever $P_1, P_2 \\subset M^\\omega$ are von Neumann subalgebras with separable predual that are globally invariant under the modular automorphism group $(\\sigma_t^{\\varphi^\\omega})$, there exist"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.5736","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":""},"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"}