{"paper":{"title":"Unified products for Leibniz algebras. Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2013-07-09T18:46:47Z","abstract_excerpt":"Let $\\mathfrak{g}$ be a Leibniz algebra and $E$ a vector space containing $\\mathfrak{g}$ as a subspace. All Leibniz algebra structures on $E$ containing $\\mathfrak{g}$ as a subalgebra are explicitly described and classified by two non-abelian cohomological type objects: ${\\mathcal H}{\\mathcal L}^{2}_{\\mathfrak{g}} \\, (V, \\, \\mathfrak{g})$ provides the classification up to an isomorphism that stabilizes $\\mathfrak{g}$ and ${\\mathcal H}{\\mathcal L}^{2} \\, (V, \\, \\mathfrak{g})$ will classify all such structures from the view point of the extension problem - here $V$ is a complement of $\\mathfrak{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2540","kind":"arxiv","version":3},"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"}