{"paper":{"title":"Braided autoequivalences and quantum commutative bi-Galois objects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Haixing Zhu, Yinhuo Zhang","submitted_at":"2013-12-13T13:05:29Z","abstract_excerpt":"Let $(H,R)$ be a quasitriangular weak Hopf algebra over a field $k$. We show that there is a braided monoidal equivalence between the Yetter-Drinfeld module category $^H_H\\mathscr{YD}$ over $H$ and the category of comodules over some braided Hopf algebra ${}_RH$ in the category $_H\\mathscr{M}$. Based on this equivalence, we prove that every braided bi-Galois object $A$ over the braided Hopf algebra ${}_RH$ defines a braided autoequivalence of the category $^H_H\\mathscr{YD}$ if and only if $A$ is quantum commutative. In case $H$ is semisimple over an algebraically closed field, i.e. the fusion "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.3800","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"}