Is the function field of a reductive Lie algebra purely transcendental over the field of invariants for the adjoint action?

DOI10.1112/S0010437X10005002zbMath1218.14010arXiv0901.4358WikidataQ115256467 ScholiaQ115256467MaRDI QIDQ2994887

Jean-Louis Colliot-Thélène, Vladimir L. Popov, Boris Kunyavskiĭ, Zinovy Reichstein

Publication date: 29 April 2011

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.4358

zbMATH Keywords

integral representation adjoint action algebraic group special groups simple Lie algebra permutation lattices rationality problem algebraic torus unramified Brauer group conjugation action transcendental extensions

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Group actions on varieties or schemes (quotients) (14L30) Integral representations of finite groups (20C10) Lie algebras of linear algebraic groups (17B45) Brauer groups of schemes (14F22) Rationality questions in algebraic geometry (14E08)

Related Items (8)

The Lie algebra of type \(G_2\) is rational over its quotient by the adjoint action ⋮ Rationality of homogeneous varieties ⋮ On the classification of normal \(G\)-varieties with spherical orbits ⋮ Cross-sections, quotients, and representation rings of semisimple algebraic groups. ⋮ The Zassenhaus variety of a reductive Lie algebra in positive characteristic ⋮ An algebraic slice in the coadjoint space of the Borel and the Coxeter element ⋮ Real reductive Cayley groups of rank 1 and 2. ⋮ Versality of algebraic group actions and rational points on twisted varieties

Cites Work

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