{"paper":{"title":"W*-superrigidity for discrete quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A family of co-induced discrete quantum groups can be recovered from their von Neumann algebras.","cross_cats":["math.GR","math.QA"],"primary_cat":"math.OA","authors_text":"Milan Donvil, Stefaan Vaes","submitted_at":"2025-04-04T08:27:39Z","abstract_excerpt":"A discrete group $G$ is called W*-superrigid if the group $G$ can be entirely recovered from the ambient group von Neumann algebra $L(G)$. We introduce an analogous notion for discrete quantum groups. We prove that this strengthened quantum W*-superrigidity property holds for a natural family of co-induced discrete quantum groups. We also prove that, remarkably, most existing families of W*-superrigid groups are not quantum W*-superrigid."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that this strengthened quantum W*-superrigidity property holds for a natural family of co-induced discrete quantum groups. We also prove that, remarkably, most existing families of W*-superrigid groups are not quantum W*-superrigid.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The specific definition of quantum W*-superrigidity is chosen so that the co-induced construction preserves the recovery property while classical W*-superrigid groups fail it; this depends on how the quantum group von Neumann algebra is defined and how co-induction interacts with it.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Introduces quantum W*-superrigidity for discrete quantum groups, proves it for co-induced families, and shows most classical W*-superrigid groups fail the quantum version.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A family of co-induced discrete quantum groups can be recovered from their von Neumann algebras.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"242adcb86ed600bcbd613eafe07c989e7c3cb5f5be92c222b511bd829994b002"},"source":{"id":"2504.03266","kind":"arxiv","version":2},"verdict":{"id":"f3f17fdf-e5f1-4f84-85d3-b8bb926410a0","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-22T21:48:06.229011Z","strongest_claim":"We prove that this strengthened quantum W*-superrigidity property holds for a natural family of co-induced discrete quantum groups. We also prove that, remarkably, most existing families of W*-superrigid groups are not quantum W*-superrigid.","one_line_summary":"Introduces quantum W*-superrigidity for discrete quantum groups, proves it for co-induced families, and shows most classical W*-superrigid groups fail the quantum version.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The specific definition of quantum W*-superrigidity is chosen so that the co-induced construction preserves the recovery property while classical W*-superrigid groups fail it; this depends on how the quantum group von Neumann algebra is defined and how co-induction interacts with it.","pith_extraction_headline":"A family of co-induced discrete quantum groups can be recovered from their von Neumann algebras."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.03266/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}