{"paper":{"title":"Groupoid normalisers of tensor products: infinite von Neumann algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Junsheng Fang, Roger R. Smith, Stuart White","submitted_at":"2010-04-06T13:43:02Z","abstract_excerpt":"The groupoid normalisers of a unital inclusion $B\\subseteq M$ of von Neumann algebras consist of the set $\\mathcal{GN}_M(B)$ of partial isometries $v\\in M$ with $vBv^*\\subseteq B$ and $v^*Bv\\subseteq B$. Given two unital inclusions $B_i\\subseteq M_i$ of von Neumann algebras, we examine groupoid normalisers for the tensor product inclusion $B_1\\ \\overline{\\otimes}\\ B_2\\subseteq M_1\\ \\overline{\\otimes}\\ M_2$ establishing the formula $$ \\mathcal{GN}_{M_1\\,\\overline{\\otimes}\\,M_2}(B_1\\ \\overline{\\otimes}\\ B_2)''=\\mathcal{GN}_{M_1}(B_1)''\\ \\overline{\\otimes}\\ \\mathcal{GN}_{M_2}(B_2)'' $$ when one i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0851","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":""},"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"}