{"paper":{"title":"Some remarks on Leibniz algebras whose semisimple part related with $sl_2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"B.A. Omirov, I.A. Karimjanov, L.M. Camacho, S. G\\'omez-Vidal","submitted_at":"2013-10-24T13:08:12Z","abstract_excerpt":"In this paper we identify the structure of complex finite-dimensional Leibniz algebras with associated Lie algebras $sl_2^1\\oplus sl_2^2\\oplus \\dots \\oplus sl_2^s\\oplus R,$ where $R$ is a solvable radical. The classifications of such Leibniz algebras in the cases $dim R=2, 3$ and $dim I\\neq 3$ have been obtained. Moreover, we classify Leibniz algebras with $L/I\\cong sl_2^1\\oplus sl_2^2$ and some conditions on ideal $I=id<[x,x] \\ | \\ x\\in L>.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6594","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"}