On the index of certain Lie algebras
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We 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 corrections
This paper is written in French. There is an english abstract. This second version contains minor corrections