The Lie Algebra of Type G2 Is Rational over Its Quotient by the Adjoint Action
نویسندگان
چکیده
Let G be a split simple group of type G2 over a field k, and let g be its Lie algebra. Answering a question of J.-L. Colliot-Thélène, B. Kunyavskĭi, V. L. Popov, and Z. Reichstein, we show that the function field k(g) is generated by algebraically independent elements over the field of adjoint invariants k(g). Résumé. Soit G un groupe algébrique simple et déployé de type G2 sur un corps k. Soit g son algèbre de Lie. On démontre que le corps des fonctions k(g) est transcendant pur sur le corps k(g) des invariants adjoints. Ceci répond par l’affirmative à une question posée par J.-L. Colliot-Thélène, B. Kunyavskĭi, V. L. Popov et Z. Reichstein.
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