{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:ZVMYPJFVD7G6CDBFQQQ52IKWYY","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":"1ec6138673490a56fc6d03c90ec2181199fd326ea5e3f0ff685c308ce778a0d1","cross_cats_sorted":["hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-09-24T15:21:38Z","title_canon_sha256":"64388c127ecde37597c65ab19dac889b9a66ab240935a3c2d50405cb6b08f920"},"schema_version":"1.0","source":{"id":"0809.4212","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4212","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4212v2","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4212","created_at":"2026-05-18T02:15:33Z"},{"alias_kind":"pith_short_12","alias_value":"ZVMYPJFVD7G6","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"ZVMYPJFVD7G6CDBF","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"ZVMYPJFV","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c9ba9cf422a11360ba51c8f130e3ad4a2f7d2da8dd95d06418344bd2f7cfdf54","target":"graph","created_at":"2026-05-18T02:15:33Z","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 construct an universal enveloping algebra associated to the ternary extension of Lie (super)algebras called Lie algebra of order three. A Poincar\\'e-Birkhoff-Witt theorem is proven is this context. It this then shown that this universal enveloping algebra can be endowed with a structure of Hopf algebra. The study of the dual of the universal enveloping algebra enables to define the parameters of the transformation of a Lie algebra of order three. It turns out that these variables are the variables which generate the three-exterior algebra.","authors_text":"M. Goze, M. Rausch de Traubenberg","cross_cats":["hep-th","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-09-24T15:21:38Z","title":"Hopf algebras for ternary algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4212","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:ed0dd3a6ee5db9e0a2c47d9720f78c60350ae795f9c54eaebdbff8c26052559f","target":"record","created_at":"2026-05-18T02:15:33Z","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":"1ec6138673490a56fc6d03c90ec2181199fd326ea5e3f0ff685c308ce778a0d1","cross_cats_sorted":["hep-th","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-09-24T15:21:38Z","title_canon_sha256":"64388c127ecde37597c65ab19dac889b9a66ab240935a3c2d50405cb6b08f920"},"schema_version":"1.0","source":{"id":"0809.4212","kind":"arxiv","version":2}},"canonical_sha256":"cd5987a4b51fcde10c258421dd2156c627013653c875265eee783a2a345b5665","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd5987a4b51fcde10c258421dd2156c627013653c875265eee783a2a345b5665","first_computed_at":"2026-05-18T02:15:33.733965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:33.733965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fIShznMpSfL14LNmWWeectPHFiRtw6Wa6R1UNqp3CEB6I9ZRlbo2Lnywlk/aPvnfrxTeExN0LiVTt1Ap5RATAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:33.734648Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.4212","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed0dd3a6ee5db9e0a2c47d9720f78c60350ae795f9c54eaebdbff8c26052559f","sha256:c9ba9cf422a11360ba51c8f130e3ad4a2f7d2da8dd95d06418344bd2f7cfdf54"],"state_sha256":"63d52467432c3bd8928b2cf504dc11ec37d84ebc1da24d5896e9552eb1ef9871"}