{"paper":{"title":"Operator-algebraic superrigidity for $SL_n(\\mathbb Z),n\\geq 3$","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Bachir Bekka","submitted_at":"2006-09-04T15:17:50Z","abstract_excerpt":"For $n\\geq 3,$ let $\\Gamma=SL_n(\\mathbb Z).$ We prove the following superridigity result for $\\Gamma$ in the context of operator algebras. Let $L(\\Gamma)$ be the von Neumann algebra generated by the left regular representation of $\\Gamma.$ Let $M$ be a finite factor and let $U(M)$ be its unitary group. Let $\\pi: \\Gamma\\to U(M)$ be a group homomorphism such that $\\pi(\\Gamma)''=M.$ Then\n  \\begin{itemize}\n  \\item[(i)] either $M$ is finite dimensional, or\n  \\item [(ii)] there exists a subgroup of finite index $\\Lambda$ of $\\Gamma$ such that $\\pi|_\\Lambda$ extends to a homomorphism $U(L(\\Lambda))\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609102","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"}