{"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"}