{"paper":{"title":"Cleft Extensions and Quotients of Twisted Quantum Doubles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GR","math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Geoffrey Mason, Siu-Hung Ng","submitted_at":"2014-04-08T06:06:29Z","abstract_excerpt":"Given a pair of finite groups $F, G$ and a normalized 3-cocycle $\\omega$ of $G$, where $F$ acts on $G$ as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension $\\Bbbk^G_\\omega\\#_c\\,\\Bbbk F$ where $c$ denotes some suitable cohomological data. When $F\\rightarrow \\overline{F}:=F/A$ is a quotient of $F$ by a central subgroup $A$ acting trivially on $G$, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type $\\Bbbk^G_\\omega\\#_c\\, \\Bbbk F\\rightarrow \\Bbbk^G_\\omega\\#_{\\overline{c}} \\, \\Bbbk \\overline{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2016","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"}