2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69113We give an upper bound for the index of certain Lie algebras, called of seaweed type, introduced by V. Dergachev, A. Kirillov and D. Panyushev. We deduce from this a conjecture of D. Panyushev stated in "Inductive formulas for the index of seaweed Lie algebra, Moscow Math. Journal (2001) 221-241". We conjecture that our upper bound gives in fact a formula for the index of such Lie algebras, and we prove it in certain cases. Finally, we obtain a result concerning the index of parabolic subalgebras of a semisimple Lie algebra.This paper is written in French. There is an english abstract. This second version contains minor correctionsRepresentation Theory17B05; 17B20text