{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:JZGHQ74UGQC4L3FAHARZYU5VS7","short_pith_number":"pith:JZGHQ74U","schema_version":"1.0","canonical_sha256":"4e4c787f943405c5eca038239c53b597e2499c444cf38c83f2a807d92be7a2bf","source":{"kind":"arxiv","id":"2406.06819","version":2},"attestation_state":"computed","paper":{"title":"Classification of almost abelian Lie groups admitting left-invariant complex or symplectic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.SG"],"primary_cat":"math.DG","authors_text":"Isabel Hern\\'andez, Mar\\'ia L. Barberis, Romina M. Arroyo, Ver\\'onica S. Diaz, Yamile Godoy","submitted_at":"2024-06-10T22:03:45Z","abstract_excerpt":"We classify the almost abelian Lie algebras $\\mathfrak g_A=\\mathbb R e_0 \\ltimes_A \\mathbb R^{2n-1}$ admitting complex or symplectic structures. The matrix $A\\in M(2n-1,\\mathbb R )$ encodes the adjoint action of $e_0$ on the abelian ideal $\\mathbb R^{2n-1}$, and the existence of complex or symplectic structures on $\\mathfrak g_A$ imposes restrictions on the Jordan normal form of $A$. The classification essentially reduces to the case when $A$ is nilpotent, so we start by considering this case. It turns out that if $A$ is nilpotent and $\\mathfrak g_A$ admits a complex structure, then $\\mathfrak"},"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":"2406.06819","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-06-10T22:03:45Z","cross_cats_sorted":["math.RA","math.SG"],"title_canon_sha256":"ab7811517977530014fbcf6412a798856f141c03a5846a803f4337b68f8289ca","abstract_canon_sha256":"9729c8a0246e95d1eb7cd83a30a55928328317a993869a482459408ab7d8a686"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:12:18.028795Z","signature_b64":"E3g/wONCbRIElffAAw5FQ8qc+GRDxC3UJL2KMQo44OZdJ+vEow0YlxVj1xm5lbpy62b2E1LD510MN+7f84DWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e4c787f943405c5eca038239c53b597e2499c444cf38c83f2a807d92be7a2bf","last_reissued_at":"2026-07-05T11:12:18.028203Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:12:18.028203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Classification of almost abelian Lie groups admitting left-invariant complex or symplectic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.SG"],"primary_cat":"math.DG","authors_text":"Isabel Hern\\'andez, Mar\\'ia L. Barberis, Romina M. Arroyo, Ver\\'onica S. Diaz, Yamile Godoy","submitted_at":"2024-06-10T22:03:45Z","abstract_excerpt":"We classify the almost abelian Lie algebras $\\mathfrak g_A=\\mathbb R e_0 \\ltimes_A \\mathbb R^{2n-1}$ admitting complex or symplectic structures. The matrix $A\\in M(2n-1,\\mathbb R )$ encodes the adjoint action of $e_0$ on the abelian ideal $\\mathbb R^{2n-1}$, and the existence of complex or symplectic structures on $\\mathfrak g_A$ imposes restrictions on the Jordan normal form of $A$. The classification essentially reduces to the case when $A$ is nilpotent, so we start by considering this case. It turns out that if $A$ is nilpotent and $\\mathfrak g_A$ admits a complex structure, then $\\mathfrak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.06819","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2406.06819/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":"2406.06819","created_at":"2026-07-05T11:12:18.028261+00:00"},{"alias_kind":"arxiv_version","alias_value":"2406.06819v2","created_at":"2026-07-05T11:12:18.028261+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.06819","created_at":"2026-07-05T11:12:18.028261+00:00"},{"alias_kind":"pith_short_12","alias_value":"JZGHQ74UGQC4","created_at":"2026-07-05T11:12:18.028261+00:00"},{"alias_kind":"pith_short_16","alias_value":"JZGHQ74UGQC4L3FA","created_at":"2026-07-05T11:12:18.028261+00:00"},{"alias_kind":"pith_short_8","alias_value":"JZGHQ74U","created_at":"2026-07-05T11:12:18.028261+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.03306","citing_title":"Almost abelian complex nilmanifolds","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7","json":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7.json","graph_json":"https://pith.science/api/pith-number/JZGHQ74UGQC4L3FAHARZYU5VS7/graph.json","events_json":"https://pith.science/api/pith-number/JZGHQ74UGQC4L3FAHARZYU5VS7/events.json","paper":"https://pith.science/paper/JZGHQ74U"},"agent_actions":{"view_html":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7","download_json":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7.json","view_paper":"https://pith.science/paper/JZGHQ74U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2406.06819&json=true","fetch_graph":"https://pith.science/api/pith-number/JZGHQ74UGQC4L3FAHARZYU5VS7/graph.json","fetch_events":"https://pith.science/api/pith-number/JZGHQ74UGQC4L3FAHARZYU5VS7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7/action/storage_attestation","attest_author":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7/action/author_attestation","sign_citation":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7/action/citation_signature","submit_replication":"https://pith.science/pith/JZGHQ74UGQC4L3FAHARZYU5VS7/action/replication_record"}},"created_at":"2026-07-05T11:12:18.028261+00:00","updated_at":"2026-07-05T11:12:18.028261+00:00"}