{"paper":{"title":"The Ribbon Elements of Drinfeld Double of Radford Hopf Algebra","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Hua Sun, Libin Li, Yuyan Zhang","submitted_at":"2024-08-19T06:58:29Z","abstract_excerpt":"Let $m$, $n$ be two positive integers, $\\Bbbk$ be an algebraically closed field with char($\\Bbbk)\\nmid mn$. Radford constructed an $mn^{2}$-dimensional Hopf algebra $R_{mn}(q)$ such that its Jacobson radical is not a Hopf ideal. We show that the Drinfeld double $D(R_{mn}(q))$ of Radford Hopf algebra $R_{mn}(q)$ has ribbon elements if and only if $n$ is odd. Moreover, if $m$ is even and $n$ is odd, then $D(R_{mn}(q))$ has two ribbon elements, if both $m$ and $n$ are odd, then $D(R_{mn}(q))$ has only one ribbon element. Finally, we compute explicitly all ribbon elements of $D(R_{mn}(q))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.09737","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.09737/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}