{"paper":{"title":"Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Boris Kunyavski\\u{i}, Jean-Louis Colliot-Th\\'el\\`ene, Vladimir L. Popov, Zinovy Reichstein","submitted_at":"2009-01-27T21:48:22Z","abstract_excerpt":"Let $k$ be a field of characteristic zero, let $G$ be a connected reductive algebraic group over $k$ and let $\\mathfrak{g}$ be its Lie algebra. Let $k(G)$, respectively, $k(\\mathfrak{g})$, be the field of $k$-rational functions on $G$, respectively, $\\mathfrak{g}$. The conjugation action of $G$ on itself induces the adjoint action of $G$ on $\\mathfrak{g}$. We investigate the question whether or not the field extensions $k(G)/k(G)^G$ and $k(\\mathfrak{g})/k(\\mathfrak{g})^G$ are purely transcendental. We show that the answer is the same for $k(G)/k(G)^G$ and $k(\\mathfrak{g})/k(\\mathfrak{g})^G$, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4358","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"}