{"paper":{"title":"Transparency condition in the categories of Yetter-Drinfel'd modules over Hopf algebras in braided categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Bojana Femi\\'c","submitted_at":"2013-03-13T00:45:59Z","abstract_excerpt":"We study versions of the categories of Yetter-Drinfel'd modules over a Hopf algebra $H$ in a braided monoidal category $\\C$. Contrarywise to Bespalov's approach, all our structures live in $\\C$. This forces $H$ to be transparent or equivalently to lie in M\\\"uger's center $\\Z_2(\\C)$ of $\\C$. We prove that versions of the categories of Yetter-Drinfel'd modules in $\\C$ are braided monoidally isomorphic to the categories of (left/right) modules over the Drinfel'd double $D(H)\\in\\C$ for $H$ finite. We obtain that these categories polarize into two disjoint groups of mutually isomorphic braided mono"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.3070","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"}