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On the index of certain Lie algebras

Patrice Tauvel·Rupert W. T. Yu
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Abstract

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.

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Patrice Tauvel, Rupert W. T. Yu. 2004-02-05. On the index of certain Lie algebras. https://arxiv.org/abs/math/0311104

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