{"paper":{"title":"Free wreath product quantum groups and standard invariants of subfactors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.OA","authors_text":"Jonas Wahl, Pierre Tarrago","submitted_at":"2016-09-07T10:58:46Z","abstract_excerpt":"By a construction of Vaughan Jones, the bipartite graph $\\Gamma(A)$ associated with the natural inclusion of $\\mathbb C$ inside a finite-dimensional $C^*$-algebra $A$ gives rise to a planar algebra $\\mathcal P^{\\Gamma(A)}$. We prove that every subfactor planar subalgebra of $\\mathcal P^{\\Gamma(A)}$ is the fixed point planar algebra of a uniquely determined action of a compact quantum group $\\mathbb G$ on $A$. We use this result to introduce a conceptual framework for the free wreath product operation on compact quantum groups in the language of planar algebras/standard invariants of subfactors"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01931","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"}