{"paper":{"title":"Some rigidity results for II$_1$ factors arising from wreath products of property (T) groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Bogdan Teodor Udrea, Ionut Chifan","submitted_at":"2018-04-12T15:09:41Z","abstract_excerpt":"We show that any infinite collection $(\\Gamma_n)_{n\\in \\mathbb N}$ of icc, hyperbolic, property (T) groups satisfies the following von Neumann algebraic \\emph{infinite product rigidity} phenomenon. If $\\Lambda$ is an arbitrary group such that $L(\\oplus_{n\\in \\mathbb N} \\Gamma_n)\\cong L(\\Lambda)$ then there exists an infinite direct sum decomposition $\\Lambda=(\\oplus_{n \\in \\mathbb N} \\Lambda_n )\\oplus A$ with $A$ icc amenable such that, for all $n\\in \\mathbb N$, up to amplifications, we have $L(\\Gamma_n) \\cong L(\\Lambda_n)$ and $L(\\oplus_{k\\geq n} \\Gamma_k )\\cong L((\\oplus_{k\\geq n} \\Lambda_k)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04558","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"}