{"paper":{"title":"Classification of Tensor Decompositions of II$_1$ Factors Associated With Poly-Hyperbolic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Rolando de Santiago, Sujan Pant","submitted_at":"2018-02-25T21:17:33Z","abstract_excerpt":"We demonstrate von Neumann algebra arising from an icc group $\\Gamma$ in Chifan's, Ioana's, and Kida's class of poly-$\\mathcal{C}_\\text{rss} $, such as a poly-hyperbolic group with no amenable factors in its composition series, satisfies the following rigidity phenomenon discovered in DHI16 (see also CdSS17): every tensor decomposition of the II$_1$ factor $L(\\Gamma) $ must arise from direct product decomposition of $\\Gamma $ by groups which are poly-$ \\mathcal{C}_\\text{rss}$. Through heavy usage and developments of the techniques in CdSS15, we improve the second author's and their collaborato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09083","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"}