{"paper":{"title":"On the Construction of Simply Connected Solvable Lie Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Mark E. Fels","submitted_at":"2013-08-04T18:37:22Z","abstract_excerpt":"Let $\\omega_\\mathfrak{g}$ be a Lie algebra valued differential $1$-form on a manifold $M$ satisfying the structure equations $d \\omega_\\mathfrak{g} + \\frac{1}{2} \\omega_\\mathfrak{g}\\wedge \\omega_\\mathfrak{g}=0$ where $\\mathfrak{g}$ is solvable. We show that the problem of finding a smooth map $\\rho:M\\to G$, where $G$ is an $n$-dimensional solvable Lie group with Lie algebra $\\mathfrak{g}$ and left invariant Maurer-Cartan form $\\tau$, such that $\\rho^* \\tau= \\omega_\\mathfrak{g}$ can be solved by quadratures and the matrix exponential. In the process we give a closed form formula for the vector "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0835","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"}