{"paper":{"title":"A note on reduced and von Neumann algebraic free wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Jonas Wahl","submitted_at":"2014-11-18T15:15:09Z","abstract_excerpt":"In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\\mathbb G \\wr_* S_N^+$, where $\\mathbb G$ is a compact matrix quantum group. Based on recent result on their corepresentation theory by Lemeux and Tarrago, we prove that $\\mathbb G \\wr_* S_N^+$ is of Kac type whenever $\\mathbb G$ is, and that the reduced version of $\\mathbb G \\wr_* S_N^+$ is simple with unique trace state whenever $N \\geq 8$. Moreover, we prove that the reduced von Neumann algebra of $\\mathbb G \\wr_* S_N^+$ does not have property $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4861","kind":"arxiv","version":1},"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"}