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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0609102","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-09-04T15:17:50Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"eb6fb3e1ff5fd58d7cb512e5a2d6091106d192d164d93036c670e9d53a6046e1","abstract_canon_sha256":"238666e9e81570a6093c24a603840fe0af9b6dff218d09864a289d340d45fb44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:59.016884Z","signature_b64":"zNYH/sFPCW3spPIHIhxrYvcgk4dK+EG335NU3VVsA1STEy/t+lOozlk/A3cTlOUMCyWZhONVTaDsJDxMRCPbAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bbbda876ebb17cf09410c79ae4742246a93505b656177127245526f988555c6d","last_reissued_at":"2026-05-18T02:27:59.016460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:59.016460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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