{"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"}