{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:NGETCTEYWVK6NLZW7BFZ6I2HBQ","short_pith_number":"pith:NGETCTEY","schema_version":"1.0","canonical_sha256":"6989314c98b555e6af36f84b9f23470c3b93de4c1c9e6dd32f3726f2e29cd841","source":{"kind":"arxiv","id":"1312.4018","version":2},"attestation_state":"computed","paper":{"title":"Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"Ana-Loredana Agore, Gigel Militaru","submitted_at":"2013-12-14T08:39:36Z","abstract_excerpt":"For a perfect Lie algebra $\\mathfrak{h}$ we classify all Lie algebras containing $\\mathfrak{h}$ as a subalgebra of codimension $1$. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product $\\mathfrak{h} \\ltimes (k^* \\times {\\rm Aut}_{\\rm Lie} (\\mathfrak{h}))$. In the non-perfect case the classification of these Lie algebras is a difficult task. Let $\\mathfrak{l} (2n+1, k)$ be the Lie algebra with the bracket $[E_i, G] = E_i$, $[G, F_i] = F_i$, for all $i = 1, \\dots, n$. We explicitly describe all Lie algebras containing $\\mathfrak{l} (2n+1, k)$ a"},"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":"1312.4018","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.RA","submitted_at":"2013-12-14T08:39:36Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"aaa6331e1dd097d6827949d3f1e025596f36c208a3810b6c200eecbcf90ebe12","abstract_canon_sha256":"d79fd5666e281f51e4076c0f04cd5fad16f6a8e380ad94c0e327f0209e32dd9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:45.753623Z","signature_b64":"MTf8rpzGxwiXEeWHlvKpOJUhxWqf2k3JSK86BPF0pW6XLQaMHCkioF/JBz36+pjcSXbOrP3KCh85ihJOnEw+CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6989314c98b555e6af36f84b9f23470c3b93de4c1c9e6dd32f3726f2e29cd841","last_reissued_at":"2026-05-18T02:49:45.753260Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:45.753260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bicrossed Products, Matched Pair Deformations and the Factorization Index for Lie Algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"Ana-Loredana Agore, Gigel Militaru","submitted_at":"2013-12-14T08:39:36Z","abstract_excerpt":"For a perfect Lie algebra $\\mathfrak{h}$ we classify all Lie algebras containing $\\mathfrak{h}$ as a subalgebra of codimension $1$. The automorphism groups of such Lie algebras are fully determined as subgroups of the semidirect product $\\mathfrak{h} \\ltimes (k^* \\times {\\rm Aut}_{\\rm Lie} (\\mathfrak{h}))$. In the non-perfect case the classification of these Lie algebras is a difficult task. Let $\\mathfrak{l} (2n+1, k)$ be the Lie algebra with the bracket $[E_i, G] = E_i$, $[G, F_i] = F_i$, for all $i = 1, \\dots, n$. We explicitly describe all Lie algebras containing $\\mathfrak{l} (2n+1, k)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4018","kind":"arxiv","version":2},"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":"1312.4018","created_at":"2026-05-18T02:49:45.753320+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4018v2","created_at":"2026-05-18T02:49:45.753320+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4018","created_at":"2026-05-18T02:49:45.753320+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGETCTEYWVK6","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGETCTEYWVK6NLZW","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGETCTEY","created_at":"2026-05-18T12:27:52.871228+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/NGETCTEYWVK6NLZW7BFZ6I2HBQ","json":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ.json","graph_json":"https://pith.science/api/pith-number/NGETCTEYWVK6NLZW7BFZ6I2HBQ/graph.json","events_json":"https://pith.science/api/pith-number/NGETCTEYWVK6NLZW7BFZ6I2HBQ/events.json","paper":"https://pith.science/paper/NGETCTEY"},"agent_actions":{"view_html":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ","download_json":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ.json","view_paper":"https://pith.science/paper/NGETCTEY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4018&json=true","fetch_graph":"https://pith.science/api/pith-number/NGETCTEYWVK6NLZW7BFZ6I2HBQ/graph.json","fetch_events":"https://pith.science/api/pith-number/NGETCTEYWVK6NLZW7BFZ6I2HBQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ/action/storage_attestation","attest_author":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ/action/author_attestation","sign_citation":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ/action/citation_signature","submit_replication":"https://pith.science/pith/NGETCTEYWVK6NLZW7BFZ6I2HBQ/action/replication_record"}},"created_at":"2026-05-18T02:49:45.753320+00:00","updated_at":"2026-05-18T02:49:45.753320+00:00"}