{"paper":{"title":"A Cohomological Proof that Real Representations of Semisimple Lie Algebras Have $\\mathbb{Q}$-Forms","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dave Witte Morris","submitted_at":"2014-10-09T02:57:26Z","abstract_excerpt":"A Lie algebra $\\mathfrak{g}_\\mathbb{Q}$ over $\\mathbb{Q}$ is said to be $\\mathbb{R}$-universal if every homomorphism from $\\mathfrak{g}_\\mathbb{Q}$ to $\\mathfrak{gl}(n,\\mathbb{R})$ is conjugate to a homomorphism into $\\mathfrak{gl}(n,\\mathbb{Q})$ (for every $n$). By using Galois cohomology, we provide a short proof of the known fact that every real semisimple Lie algebra has an $\\mathbb{R}$-universal $\\mathbb{Q}$-form. We also provide a classification of the $\\mathbb{R}$-universal Lie algebras that are semisimple."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2339","kind":"arxiv","version":5},"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"}