{"paper":{"title":"Transmutation Theory and Quantization Approach for Quantum Groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Tao Yang, Xuan Zhou","submitted_at":"2011-11-06T10:32:01Z","abstract_excerpt":"Let $H$ and $L$ be quantum groupoids. If $H$ has a quasitriangular structure, then we show that $L$ induces a Hopf algebra $C_{L}(L_s)$ in the category $_{H}\\mathcal{M}$, which generalizes the transmutation theory introduced by Majid. Furthermore, if $H$ is commutative, we can construct a Hopf algebra $C_H(H_s)_F$ in the category $_H\\mathcal{M}_F$ for a weak invertible unit 2-cocycle $F$, which generalizes the results in \\cite{D83}. Finally, we consider the relation between two Hopf algebras: $C_H(H_s)_F$ and $C_{\\widetilde H}(\\widetilde{H}_s)$, and obtain that they are isomorphic as objects i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.1397","kind":"arxiv","version":3},"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"}