J.-L. Colliot-Thélène: A rationality question for the adjoint group

Summary : Let G be a simple algebraic group over the complex field, let g be its Lie algebra. We investigate the question whether the field of rational functions of g is purely transcendental over the subfield of invariant rational functions for the adjoint representation of G on g. This is joint work with B. Kunyavskii, V. L. Popov and Z. Reichstein.