Group theory/Algebraic geometry
The Lie algebra of type G2 is rational over its quotient by the adjoint action
Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 871-875.

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. Kunyavskiĭ, 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)G.

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)G des invariants adjoints. Ceci répond par lʼaffirmative à une question posée par J.-L. Colliot-Thélène, B. Kunyavskiĭ, V.L. Popov et Z. Reichstein.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2013.10.029
Anderson, Dave 1; Florence, Mathieu 2; Reichstein, Zinovy 3

1 Instituto Nacional de Matemática Pura e Aplicada, Rio de Janeiro, RJ 22460-320, Brazil
2 Institut de mathématiques de Jussieu, Université Paris-6, 4, place Jussieu, 75005 Paris, France
3 Department of Mathematics, University of British Columbia, BC V6T 1Z2, Canada
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Anderson, Dave; Florence, Mathieu; Reichstein, Zinovy. The Lie algebra of type $ {G}_{2}$ is rational over its quotient by the adjoint action. Comptes Rendus. Mathématique, Volume 351 (2013) no. 23-24, pp. 871-875. doi : 10.1016/j.crma.2013.10.029. http://www.numdam.org/articles/10.1016/j.crma.2013.10.029/

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Cited by Sources:

D.A. was partially supported by NSF Grant DMS-0902967. Z.R. was partially supported by National Sciences and Engineering Research Council of Canada Grant No. 250217-2012.