{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:ZBLIZM72RGRLYBRDNLMMC7NZER","short_pith_number":"pith:ZBLIZM72","schema_version":"1.0","canonical_sha256":"c8568cb3fa89a2bc06236ad8c17db9247496da8b743ff7095eadf19f0d30008b","source":{"kind":"arxiv","id":"0902.2821","version":1},"attestation_state":"computed","paper":{"title":"Quantizations of generalized Cartan type $S$ Lie algebras and of the special algebra $\\mathbf{S}(n;\\underline{1})$ in the modular case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Naihong Hu, Xiuling Wang","submitted_at":"2009-02-17T02:35:48Z","abstract_excerpt":"The generalized Cartan type $\\mathbf{S}$ Lie algebras in char 0 with the Lie bialgebra structures involved are quantized, where the Drinfel'd twist we used is proved to be a variation of the Jordanian twist. As the passage from char 0 to char p, their quantization integral forms are given. By the modular reduction and base changes, we obtain certain quantizations of the restricted universal enveloping algebra $\\mathbf u(\\mathbf{S}(n;\\underline{1}))$ (for the Cartan type simple modular restricted Lie algebra $\\mathbf{S}(n;\\underline{1})$ of $\\mathbf{S}$ type). They are new Hopf algebras of trun"},"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":"0902.2821","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2009-02-17T02:35:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"14368ffc9ebb0a2dba6702e4eaae0786bd06f1b40a2dcb00022e9e4c3c16c230","abstract_canon_sha256":"cc0577816cd9592c3300fdd56c479e17500ef4beba8d3dd836b0447015249029"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:10.462992Z","signature_b64":"6Qf7KfBw0AEhyvwmJpMuhFHV/SZBezAuDSm8jLlKusC5PdnNnevzCpAMzbAHsbBmni0abbRQY6PEj9kCK0gxCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c8568cb3fa89a2bc06236ad8c17db9247496da8b743ff7095eadf19f0d30008b","last_reissued_at":"2026-05-18T02:41:10.462417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:10.462417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantizations of generalized Cartan type $S$ Lie algebras and of the special algebra $\\mathbf{S}(n;\\underline{1})$ in the modular case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Naihong Hu, Xiuling Wang","submitted_at":"2009-02-17T02:35:48Z","abstract_excerpt":"The generalized Cartan type $\\mathbf{S}$ Lie algebras in char 0 with the Lie bialgebra structures involved are quantized, where the Drinfel'd twist we used is proved to be a variation of the Jordanian twist. As the passage from char 0 to char p, their quantization integral forms are given. By the modular reduction and base changes, we obtain certain quantizations of the restricted universal enveloping algebra $\\mathbf u(\\mathbf{S}(n;\\underline{1}))$ (for the Cartan type simple modular restricted Lie algebra $\\mathbf{S}(n;\\underline{1})$ of $\\mathbf{S}$ type). They are new Hopf algebras of trun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.2821","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":""},"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":"0902.2821","created_at":"2026-05-18T02:41:10.462496+00:00"},{"alias_kind":"arxiv_version","alias_value":"0902.2821v1","created_at":"2026-05-18T02:41:10.462496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.2821","created_at":"2026-05-18T02:41:10.462496+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZBLIZM72RGRL","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZBLIZM72RGRLYBRD","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZBLIZM72","created_at":"2026-05-18T12:26:02.257875+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/ZBLIZM72RGRLYBRDNLMMC7NZER","json":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER.json","graph_json":"https://pith.science/api/pith-number/ZBLIZM72RGRLYBRDNLMMC7NZER/graph.json","events_json":"https://pith.science/api/pith-number/ZBLIZM72RGRLYBRDNLMMC7NZER/events.json","paper":"https://pith.science/paper/ZBLIZM72"},"agent_actions":{"view_html":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER","download_json":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER.json","view_paper":"https://pith.science/paper/ZBLIZM72","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0902.2821&json=true","fetch_graph":"https://pith.science/api/pith-number/ZBLIZM72RGRLYBRDNLMMC7NZER/graph.json","fetch_events":"https://pith.science/api/pith-number/ZBLIZM72RGRLYBRDNLMMC7NZER/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER/action/storage_attestation","attest_author":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER/action/author_attestation","sign_citation":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER/action/citation_signature","submit_replication":"https://pith.science/pith/ZBLIZM72RGRLYBRDNLMMC7NZER/action/replication_record"}},"created_at":"2026-05-18T02:41:10.462496+00:00","updated_at":"2026-05-18T02:41:10.462496+00:00"}