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Specifically, assume that $G=A\\times W$, where $A$ is an infinite abelian group and $W$ is an ICC wreath-like product group [CIOS22a; AMCOS23] with property (T) and trivial abelianization. Then whenever $H$ is an \\emph{arbitrary} group such that $\\mathcal{L}(G)$ is $\\ast$-isomorphic to $\\mathcal L(H)$ it must be the case that $H= B \\times H_0$ where $B$ is infinite abelian and $H_0$ is isomorphic to $W$. Moreover, we complete"},"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":"2403.01280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-03-02T18:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"628352bf1b3f34bcdeca7f8977060337cae301c10aa5ddd8f485502974d6a1ad","abstract_canon_sha256":"b1e87a4d88ce49065421dc50f4d79c25e60d5a1fd6debf5cfd55ef9b69ba4631"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:20:41.325877Z","signature_b64":"KkW+icaONQnl1tdN+PwnU2PQlobk+uNo29gD0Jq63fMmE8JCMCt6qLD3voOu5sFacsRTg5Iz+q7QHuRXUErHBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdd9ef7d945ee5514a389e3d1a4131ced76f63c659d43b3de7836b859a7b750e","last_reissued_at":"2026-07-05T09:20:41.325403Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:20:41.325403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity results for group von Neumann algebras with diffuse center","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adriana Fern\\'andez Quero, Hui Tan, Ionu\\c{t} Chifan","submitted_at":"2024-03-02T18:25:30Z","abstract_excerpt":"We introduce the first examples of groups $G$ with infinite center which in a natural sense are completely recognizable from their von Neumann algebras, $\\mathcal{L}(G)$. Specifically, assume that $G=A\\times W$, where $A$ is an infinite abelian group and $W$ is an ICC wreath-like product group [CIOS22a; AMCOS23] with property (T) and trivial abelianization. Then whenever $H$ is an \\emph{arbitrary} group such that $\\mathcal{L}(G)$ is $\\ast$-isomorphic to $\\mathcal L(H)$ it must be the case that $H= B \\times H_0$ where $B$ is infinite abelian and $H_0$ is isomorphic to $W$. 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