Index and stable linear forms of Lie algebras

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66446We characterize, in a purely algebraic manner, certain linear forms, called stable, on a Lie algebra. As an application, we determine the index of a Borel subalgebra of a semi-simple Lie algebra. Finally, we give an example of a parabolic subalgebra of a semi-simple Lie algebra which does not admit any stable linear form.This paper is written in FrenchRepresentation Theory17B45; 17B20Index and stable linear forms of Lie algebrastext