{"paper":{"title":"Galois groups and group actions on Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2015-05-27T14:37:04Z","abstract_excerpt":"If $\\mathfrak{g} \\subseteq \\mathfrak{h}$ is an extension of Lie algebras over a field $k$ such that ${\\rm dim}_k (\\mathfrak{g}) = n$ and ${\\rm dim}_k (\\mathfrak{h}) = n + m$, then the Galois group ${\\rm Gal} \\, (\\mathfrak{h}/\\mathfrak{g})$ is explicitly described as a subgroup of the canonical semidirect product of groups ${\\rm GL} (m, \\, k) \\rtimes {\\rm M}_{n\\times m} (k)$. An Artin type theorem for Lie algebras is proved: if a group $G$ whose order isinvertible in $k$ acts as automorphisms on a Lie algebra $\\mathfrak{h}$, then $\\mathfrak{h}$ is isomorphic to a skew crossed product $\\mathfrak"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07346","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"}