{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:IYBNLN3F5MICCYKEHSRXPILE4O","short_pith_number":"pith:IYBNLN3F","schema_version":"1.0","canonical_sha256":"4602d5b765eb102161443ca377a164e3ba7cea49629502ff4dc3b347e88e7a10","source":{"kind":"arxiv","id":"1009.3541","version":2},"attestation_state":"computed","paper":{"title":"Structure of semisimple Hopf algebras of dimension $p^2q^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Jingcheng Dong","submitted_at":"2010-09-18T09:15:25Z","abstract_excerpt":"Let $p,q$ be prime numbers with $p^4<q$, and $k$ an algebraically closed field of characteristic 0. We show that semisimple Hopf algebras of dimension $p^2q^2$ can be constructed either from group algebras and their duals by means of extensions, or from Radford biproduct $R#kG$, where $kG$ is the group algebra of group $G$ of order $p^2$, $R$ is a semisimple Yetter-Drinfeld Hopf algebra in ${}^{kG}_{kG}\\mathcal{YD}$ of dimension $q^2$. As an application, the special case that the structure of semisimple Hopf algebras of dimension $4q^2$ is given."},"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":"1009.3541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2010-09-18T09:15:25Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"a164bc27cc10bd4fc8728b75236d00dc1fba2becd0fd2bbc2745fdc11d6c2bd9","abstract_canon_sha256":"7e9f9bb3ca9b1d78870fe9b97776c6c98509f583d4f82930fca0277e2ae15d1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:04.672430Z","signature_b64":"+R0hmFJx4xl+OPzUYF1poABFhipwfFQ3Wh5OSs5mp6YK2pqBtZeXkbmxB5GWO5LfQpfCgCLK/ImVc3hr/6XABw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4602d5b765eb102161443ca377a164e3ba7cea49629502ff4dc3b347e88e7a10","last_reissued_at":"2026-05-18T03:58:04.671950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:04.671950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structure of semisimple Hopf algebras of dimension $p^2q^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Jingcheng Dong","submitted_at":"2010-09-18T09:15:25Z","abstract_excerpt":"Let $p,q$ be prime numbers with $p^4<q$, and $k$ an algebraically closed field of characteristic 0. We show that semisimple Hopf algebras of dimension $p^2q^2$ can be constructed either from group algebras and their duals by means of extensions, or from Radford biproduct $R#kG$, where $kG$ is the group algebra of group $G$ of order $p^2$, $R$ is a semisimple Yetter-Drinfeld Hopf algebra in ${}^{kG}_{kG}\\mathcal{YD}$ of dimension $q^2$. As an application, the special case that the structure of semisimple Hopf algebras of dimension $4q^2$ is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3541","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.3541","created_at":"2026-05-18T03:58:04.672036+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3541v2","created_at":"2026-05-18T03:58:04.672036+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3541","created_at":"2026-05-18T03:58:04.672036+00:00"},{"alias_kind":"pith_short_12","alias_value":"IYBNLN3F5MIC","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"IYBNLN3F5MICCYKE","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"IYBNLN3F","created_at":"2026-05-18T12:26:09.077623+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/IYBNLN3F5MICCYKEHSRXPILE4O","json":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O.json","graph_json":"https://pith.science/api/pith-number/IYBNLN3F5MICCYKEHSRXPILE4O/graph.json","events_json":"https://pith.science/api/pith-number/IYBNLN3F5MICCYKEHSRXPILE4O/events.json","paper":"https://pith.science/paper/IYBNLN3F"},"agent_actions":{"view_html":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O","download_json":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O.json","view_paper":"https://pith.science/paper/IYBNLN3F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3541&json=true","fetch_graph":"https://pith.science/api/pith-number/IYBNLN3F5MICCYKEHSRXPILE4O/graph.json","fetch_events":"https://pith.science/api/pith-number/IYBNLN3F5MICCYKEHSRXPILE4O/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O/action/storage_attestation","attest_author":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O/action/author_attestation","sign_citation":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O/action/citation_signature","submit_replication":"https://pith.science/pith/IYBNLN3F5MICCYKEHSRXPILE4O/action/replication_record"}},"created_at":"2026-05-18T03:58:04.672036+00:00","updated_at":"2026-05-18T03:58:04.672036+00:00"}