{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6L5JVUUBS4VPCDPP6MNNAWLCC5","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"87ded5e561e927cda68a9ca61e5afe9a4faf79ae3977a7600474c07574842eb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-01T05:30:25Z","title_canon_sha256":"732b6227dbb51c4b85f1bdc1bef84f1b068abf4ab98501e76a33890659ed976f"},"schema_version":"1.0","source":{"id":"1312.0178","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0178","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0178v2","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0178","created_at":"2026-05-18T00:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"6L5JVUUBS4VP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6L5JVUUBS4VPCDPP","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6L5JVUUB","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:de3689c4291e2ac5b2e89f4224eb9d1460e30bc9beb3fec6839c1079b54f094a","target":"graph","created_at":"2026-05-18T00:27:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We derive necessary and sufficient conditions for an Ore extension of a Hopf algebra to have a Hopf algebra structure of a certain type. This construction generalizes the notion of Hopf-Ore extension, called a generalized Hopf-Ore extension. We describe the generalized Hopf-Ore extensions of the enveloping algebras of Lie algebras. For some Lie algebras g, the generalized Hopf-Ore extensions of U(g) are classified.","authors_text":"Huixiang Chen, Lan You, Zhen Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-01T05:30:25Z","title":"Generalized Hopf-Ore extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0178","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:557ef613a199fff58b9fff53fff789e5554f4a1c8a848a24b668590d82a7d37f","target":"record","created_at":"2026-05-18T00:27:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"87ded5e561e927cda68a9ca61e5afe9a4faf79ae3977a7600474c07574842eb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-12-01T05:30:25Z","title_canon_sha256":"732b6227dbb51c4b85f1bdc1bef84f1b068abf4ab98501e76a33890659ed976f"},"schema_version":"1.0","source":{"id":"1312.0178","kind":"arxiv","version":2}},"canonical_sha256":"f2fa9ad281972af10deff31ad0596217779a453929fa312f9624e3d231c76e76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2fa9ad281972af10deff31ad0596217779a453929fa312f9624e3d231c76e76","first_computed_at":"2026-05-18T00:27:03.284120Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:27:03.284120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Le9p9PqYMjLBoOwTJ2J7+NVpTtA5K9ypMuT35TstaTh7j8lxtYbe07kS7du+wn4EEFqhME4JcAm91jKW4tUBBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:27:03.284723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0178","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:557ef613a199fff58b9fff53fff789e5554f4a1c8a848a24b668590d82a7d37f","sha256:de3689c4291e2ac5b2e89f4224eb9d1460e30bc9beb3fec6839c1079b54f094a"],"state_sha256":"11a197bd3b3a1a8b5f387fa5b959efab0e09a72cdfa6823436b24a471c7f4c77"}