{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:AGZCTVRORLMXWD5SYAEUBZIDRJ","short_pith_number":"pith:AGZCTVRO","schema_version":"1.0","canonical_sha256":"01b229d62e8ad97b0fb2c00940e5038a5355e94907a187773496941eaff8498e","source":{"kind":"arxiv","id":"0806.0978","version":4},"attestation_state":"computed","paper":{"title":"Twisted exterior derivatives for universal enveloping algebras I","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Zoran \\v{S}koda","submitted_at":"2008-06-05T14:24:17Z","abstract_excerpt":"Consider any representation $\\phi$ of a finite-dimensional Lie algebra $g$ by derivations of the completed symmetric algebra $\\hat{S}(g^*)$ of its dual. Consider the tensor product of $\\hat{S}(g^*)$ and the exterior algebra $\\Lambda(g)$. We show that the representation $\\phi$ extends canonically to the representation $\\tilde\\phi$ of that tensor product algebra. We construct an exterior derivative on that algebra, giving rise to a twisted version of the exterior differential calculus with the enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators betw"},"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":"0806.0978","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.QA","submitted_at":"2008-06-05T14:24:17Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"d36c936469f590a28448056acbca7ee87ed6a3f449363470a689172e17bc1145","abstract_canon_sha256":"b1876d0dcd4fa02939ff50d1e14e2c2c0279b5053f96a638d7ea6b08ebe16f80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:27:15.805267Z","signature_b64":"YqahHagSPtHFLtY2gE3kFx9Jxhn3HSsjO7ZoiHoPwHFD8DE6/CA20X8FM1e/5PO2FCMehTY7k22bf+e23qFVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01b229d62e8ad97b0fb2c00940e5038a5355e94907a187773496941eaff8498e","last_reissued_at":"2026-07-05T01:27:15.804860Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:27:15.804860Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twisted exterior derivatives for universal enveloping algebras I","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"Zoran \\v{S}koda","submitted_at":"2008-06-05T14:24:17Z","abstract_excerpt":"Consider any representation $\\phi$ of a finite-dimensional Lie algebra $g$ by derivations of the completed symmetric algebra $\\hat{S}(g^*)$ of its dual. Consider the tensor product of $\\hat{S}(g^*)$ and the exterior algebra $\\Lambda(g)$. We show that the representation $\\phi$ extends canonically to the representation $\\tilde\\phi$ of that tensor product algebra. We construct an exterior derivative on that algebra, giving rise to a twisted version of the exterior differential calculus with the enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators betw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0806.0978","kind":"arxiv","version":4},"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/0806.0978/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":"0806.0978","created_at":"2026-07-05T01:27:15.804918+00:00"},{"alias_kind":"arxiv_version","alias_value":"0806.0978v4","created_at":"2026-07-05T01:27:15.804918+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0806.0978","created_at":"2026-07-05T01:27:15.804918+00:00"},{"alias_kind":"pith_short_12","alias_value":"AGZCTVRORLMX","created_at":"2026-07-05T01:27:15.804918+00:00"},{"alias_kind":"pith_short_16","alias_value":"AGZCTVRORLMXWD5S","created_at":"2026-07-05T01:27:15.804918+00:00"},{"alias_kind":"pith_short_8","alias_value":"AGZCTVRO","created_at":"2026-07-05T01:27:15.804918+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.03125","citing_title":"Examples of scalar extension Hopf algebroids over a universal enveloping algebra","ref_index":19,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ","json":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ.json","graph_json":"https://pith.science/api/pith-number/AGZCTVRORLMXWD5SYAEUBZIDRJ/graph.json","events_json":"https://pith.science/api/pith-number/AGZCTVRORLMXWD5SYAEUBZIDRJ/events.json","paper":"https://pith.science/paper/AGZCTVRO"},"agent_actions":{"view_html":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ","download_json":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ.json","view_paper":"https://pith.science/paper/AGZCTVRO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0806.0978&json=true","fetch_graph":"https://pith.science/api/pith-number/AGZCTVRORLMXWD5SYAEUBZIDRJ/graph.json","fetch_events":"https://pith.science/api/pith-number/AGZCTVRORLMXWD5SYAEUBZIDRJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ/action/storage_attestation","attest_author":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ/action/author_attestation","sign_citation":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ/action/citation_signature","submit_replication":"https://pith.science/pith/AGZCTVRORLMXWD5SYAEUBZIDRJ/action/replication_record"}},"created_at":"2026-07-05T01:27:15.804918+00:00","updated_at":"2026-07-05T01:27:15.804918+00:00"}