{"paper":{"title":"The Lie algebra of type G_2 is rational over its quotient by the adjoint action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Dave Anderson, Mathieu Florence, Zinovy Reichstein","submitted_at":"2013-08-27T18:17:07Z","abstract_excerpt":"Let G be a split simple group of type G_2 over a field k, and let g be its Lie algebra. Answering a question of Colliot-Th\\'el\\`ene, Kunyavski\\u{i}, Popov, and Reichstein, we show that the function field k(g) is generated by algebraically independent elements over the field of adjoint invariants k(g)^G.\n  Soit G un groupe alg\\'ebrique simple et d\\'eploy\\'e de type G_2 sur un corps k. Soit g son alg\\`ebre de Lie. On d\\'emontre que le corps des fonctions k(g) est transcendant pur sur le corps k(g)^G des invariants adjoints. Ceci r\\'epond par l'affirmative \\`a une question pos\\'ee par Colliot-Th\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5940","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"}