{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:AW255SJIHCM7EPDWFAPNZLPFYO","short_pith_number":"pith:AW255SJI","schema_version":"1.0","canonical_sha256":"05b5dec9283899f23c76281edcade5c3b05821c81be09895089c1448a975ae79","source":{"kind":"arxiv","id":"1906.09979","version":1},"attestation_state":"computed","paper":{"title":"Manin triples of 3-Lie algebras induced by involutive derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Ruipu Bai, Shuai Hou","submitted_at":"2019-06-21T13:14:38Z","abstract_excerpt":"For any $n$-dimensional 3-Lie algebra $A$ over a field of characteristic zero with an involutive derivation $D$, we investigate the structure of the 3-Lie algebra $B_1=A\\ltimes_{ad^*} A^* $ associated with the coadjoint representation $(A^*, ad^*)$. We then discuss the structure of the dual 3-Lie algebra $B_2$ of the local cocycle 3-Lie bialgebra $(A\\ltimes_{ad^*} A^*, \\Delta)$. By means of the involutive derivation $D$, we construct the $4n$-dimensional Manin triple $(B_1\\oplus B_2,$ $ [ \\cdot, \\cdot, \\cdot]_1,$ $ [ \\cdot, \\cdot, \\cdot]_2,$ $ B_1, B_2)$ of 3-Lie algebras, and provide concrete"},"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":"1906.09979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-06-21T13:14:38Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4c2bf144b399d8a3d7cc094830d19dbf1e1871cec10b9fb4405f546b46f543c3","abstract_canon_sha256":"0a1d3718499dc614873b1a08e054c27ad8d2e65c79011ebcb2e9f484958b6a33"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:35.870238Z","signature_b64":"ZdMp5N0HovzZZ0tH34dhBJBb5TgRB6k4VAmz2LmdMT4BEAaov56VAF00GswlxW+Ds+Evh0ajdCTchXkPvrK+AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05b5dec9283899f23c76281edcade5c3b05821c81be09895089c1448a975ae79","last_reissued_at":"2026-05-17T23:42:35.869498Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:35.869498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Manin triples of 3-Lie algebras induced by involutive derivations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RA","authors_text":"Ruipu Bai, Shuai Hou","submitted_at":"2019-06-21T13:14:38Z","abstract_excerpt":"For any $n$-dimensional 3-Lie algebra $A$ over a field of characteristic zero with an involutive derivation $D$, we investigate the structure of the 3-Lie algebra $B_1=A\\ltimes_{ad^*} A^* $ associated with the coadjoint representation $(A^*, ad^*)$. We then discuss the structure of the dual 3-Lie algebra $B_2$ of the local cocycle 3-Lie bialgebra $(A\\ltimes_{ad^*} A^*, \\Delta)$. By means of the involutive derivation $D$, we construct the $4n$-dimensional Manin triple $(B_1\\oplus B_2,$ $ [ \\cdot, \\cdot, \\cdot]_1,$ $ [ \\cdot, \\cdot, \\cdot]_2,$ $ B_1, B_2)$ of 3-Lie algebras, and provide concrete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.09979","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":"1906.09979","created_at":"2026-05-17T23:42:35.869628+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.09979v1","created_at":"2026-05-17T23:42:35.869628+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.09979","created_at":"2026-05-17T23:42:35.869628+00:00"},{"alias_kind":"pith_short_12","alias_value":"AW255SJIHCM7","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"AW255SJIHCM7EPDW","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"AW255SJI","created_at":"2026-05-18T12:33:12.712433+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/AW255SJIHCM7EPDWFAPNZLPFYO","json":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO.json","graph_json":"https://pith.science/api/pith-number/AW255SJIHCM7EPDWFAPNZLPFYO/graph.json","events_json":"https://pith.science/api/pith-number/AW255SJIHCM7EPDWFAPNZLPFYO/events.json","paper":"https://pith.science/paper/AW255SJI"},"agent_actions":{"view_html":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO","download_json":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO.json","view_paper":"https://pith.science/paper/AW255SJI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.09979&json=true","fetch_graph":"https://pith.science/api/pith-number/AW255SJIHCM7EPDWFAPNZLPFYO/graph.json","fetch_events":"https://pith.science/api/pith-number/AW255SJIHCM7EPDWFAPNZLPFYO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO/action/storage_attestation","attest_author":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO/action/author_attestation","sign_citation":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO/action/citation_signature","submit_replication":"https://pith.science/pith/AW255SJIHCM7EPDWFAPNZLPFYO/action/replication_record"}},"created_at":"2026-05-17T23:42:35.869628+00:00","updated_at":"2026-05-17T23:42:35.869628+00:00"}