{"paper":{"title":"Trivial Central Extensions of Lie Bialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"A. Patricia Jancsa, Marco A. Farinati","submitted_at":"2011-10-05T18:58:07Z","abstract_excerpt":"From a Lie algebra $\\mathfrak{g}$ satisfying $\\mathcal{Z}(\\mathfrak{g})=0$ and $\\Lambda^2(\\mathfrak{g})^\\mathfrak{g}=0$ (in particular, for $\\g$ semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form $\\mathfrak{L} =\\mathfrak{g}\\times \\mathbb{K}$ in terms of Lie bialgebra structures on $\\mathfrak{g}$ (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field $\\mathbb{K}$ with char $\\mathbb{K}=0$. If moreover, $[\\mathfrak{g},\\mathfrak{g}]=\\mathfrak{g}$, then we describe also all Lie bialgebra structures on extensions $\\mathfrak{L} "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1072","kind":"arxiv","version":1},"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"}