{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:QRF27A5XUL2RHXIS2ALOU2UFNJ","short_pith_number":"pith:QRF27A5X","schema_version":"1.0","canonical_sha256":"844baf83b7a2f513dd12d016ea6a856a57f6b0cf2eb11af3abc2a0c8730040f2","source":{"kind":"arxiv","id":"1309.7442","version":3},"attestation_state":"computed","paper":{"title":"Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hui-Xiang Chen, Lan You, Zhen Wang","submitted_at":"2013-09-28T09:01:24Z","abstract_excerpt":"In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let $H=kG(\\chi, a,\\d)$ be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\\chi$ is a $k$-valued character for $G$ with $\\chi(a)\\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consid"},"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":"1309.7442","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-09-28T09:01:24Z","cross_cats_sorted":[],"title_canon_sha256":"c2ac149318200e9fa0dc95569bcca2ad345ea4760e094cca13b1d46ee8c5fa56","abstract_canon_sha256":"2e5ef1604ac14fea3b19923a65c4f7125488cc7a9268147dce9d6f450c365d54"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:29.430680Z","signature_b64":"5ntG0pysAfMtjWOzyQXNXqNp8gj/vPHdCUdlzzObau/WuxrYVIbeum5js5qdIbTp65ojDmVeOs6nTajkuVi+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"844baf83b7a2f513dd12d016ea6a856a57f6b0cf2eb11af3abc2a0c8730040f2","last_reissued_at":"2026-05-18T00:14:29.430044Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:29.430044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representations of Hopf Ore extensions of group algebras and pointed Hopf algebras of rank one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Hui-Xiang Chen, Lan You, Zhen Wang","submitted_at":"2013-09-28T09:01:24Z","abstract_excerpt":"In this paper, we study the representation theory of Hopf-Ore extensions of group algebras and pointed Hopf algebras of rank one over an arbitrary field $k$. Let $H=kG(\\chi, a,\\d)$ be a Hopf-Ore extension of $kG$ and $H'$ a rank one quotient Hopf algebra of $H$, where $k$ is a field, $G$ is a group, $a$ is a central element of $G$ and $\\chi$ is a $k$-valued character for $G$ with $\\chi(a)\\neq 1$. We first show that the simple weight modules over $H$ and $H'$ are finite dimensional. Then we describe the structures of all simple weight modules over $H$ and $H'$, and classify them. We also consid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7442","kind":"arxiv","version":3},"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":"1309.7442","created_at":"2026-05-18T00:14:29.430129+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7442v3","created_at":"2026-05-18T00:14:29.430129+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7442","created_at":"2026-05-18T00:14:29.430129+00:00"},{"alias_kind":"pith_short_12","alias_value":"QRF27A5XUL2R","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_16","alias_value":"QRF27A5XUL2RHXIS","created_at":"2026-05-18T12:27:57.521954+00:00"},{"alias_kind":"pith_short_8","alias_value":"QRF27A5X","created_at":"2026-05-18T12:27:57.521954+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/QRF27A5XUL2RHXIS2ALOU2UFNJ","json":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ.json","graph_json":"https://pith.science/api/pith-number/QRF27A5XUL2RHXIS2ALOU2UFNJ/graph.json","events_json":"https://pith.science/api/pith-number/QRF27A5XUL2RHXIS2ALOU2UFNJ/events.json","paper":"https://pith.science/paper/QRF27A5X"},"agent_actions":{"view_html":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ","download_json":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ.json","view_paper":"https://pith.science/paper/QRF27A5X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7442&json=true","fetch_graph":"https://pith.science/api/pith-number/QRF27A5XUL2RHXIS2ALOU2UFNJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QRF27A5XUL2RHXIS2ALOU2UFNJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ/action/storage_attestation","attest_author":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ/action/author_attestation","sign_citation":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ/action/citation_signature","submit_replication":"https://pith.science/pith/QRF27A5XUL2RHXIS2ALOU2UFNJ/action/replication_record"}},"created_at":"2026-05-18T00:14:29.430129+00:00","updated_at":"2026-05-18T00:14:29.430129+00:00"}