{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:AYYX666PJEDYTXSG6RIJPNQDGS","short_pith_number":"pith:AYYX666P","schema_version":"1.0","canonical_sha256":"06317f7bcf490789de46f45097b60334933ae0ecce76f0dc59e3b2b2018ae3e7","source":{"kind":"arxiv","id":"2408.09737","version":1},"attestation_state":"computed","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 $D(R_{mn}(q))$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2408.09737","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2024-08-19T06:58:29Z","cross_cats_sorted":[],"title_canon_sha256":"24f85966c29cf52d22e105a8e0ee0db6aca461679789344c9ea972deb7f1816a","abstract_canon_sha256":"46cec2a8cebe010cb74c0f8006aff2b8b7befa589741bbe4712dcb60c59c6c11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:56:36.381064Z","signature_b64":"0Go4xIIxtMbdw8yaCELAop8jBs/emIkfL6O8FVnPKjmjvS7vgqbX9VcU3cP2ydMamBwLs0vnyPrjUl9S4hmsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06317f7bcf490789de46f45097b60334933ae0ecce76f0dc59e3b2b2018ae3e7","last_reissued_at":"2026-07-05T08:56:36.380603Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:56:36.380603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2408.09737","created_at":"2026-07-05T08:56:36.380670+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.09737v1","created_at":"2026-07-05T08:56:36.380670+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.09737","created_at":"2026-07-05T08:56:36.380670+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYYX666PJEDY","created_at":"2026-07-05T08:56:36.380670+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYYX666PJEDYTXSG","created_at":"2026-07-05T08:56:36.380670+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYYX666P","created_at":"2026-07-05T08:56:36.380670+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS","json":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS.json","graph_json":"https://pith.science/api/pith-number/AYYX666PJEDYTXSG6RIJPNQDGS/graph.json","events_json":"https://pith.science/api/pith-number/AYYX666PJEDYTXSG6RIJPNQDGS/events.json","paper":"https://pith.science/paper/AYYX666P"},"agent_actions":{"view_html":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS","download_json":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS.json","view_paper":"https://pith.science/paper/AYYX666P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.09737&json=true","fetch_graph":"https://pith.science/api/pith-number/AYYX666PJEDYTXSG6RIJPNQDGS/graph.json","fetch_events":"https://pith.science/api/pith-number/AYYX666PJEDYTXSG6RIJPNQDGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS/action/storage_attestation","attest_author":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS/action/author_attestation","sign_citation":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS/action/citation_signature","submit_replication":"https://pith.science/pith/AYYX666PJEDYTXSG6RIJPNQDGS/action/replication_record"}},"created_at":"2026-07-05T08:56:36.380670+00:00","updated_at":"2026-07-05T08:56:36.380670+00:00"}