Sur l'indice de certaines algèbres de Lie  [ On the index of certain Lie algebras ]
Annales de l'Institut Fourier, Volume 54 (2004) no. 6, p. 1793-1810

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. 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.

On donne une majoration de l'indice de certaines algèbres de Lie introduites par V. Dergachev, A. Kirillov et D. Panyushev. On en déduit la preuve d'une conjecture de D. Panyushev. Nous formulons aussi une conjecture concernant l'indice de ces algèbres, et la prouvons dans des cas particuliers. Enfin, nous donnons un résultat concernant l'indice des sous-algèbres paraboliques d'une algèbre de Lie semi-simple.

DOI : https://doi.org/10.5802/aif.2066
Classification:  17B05,  17B20
Keywords: semisimple lie algebras, seaweed lie algebras, index
@article{AIF_2004__54_6_1793_0,
     author = {Tauvel, Patrice and Yu, Rupert W.T.},
     title = {Sur l'indice de certaines alg\`ebres de Lie},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {54},
     number = {6},
     year = {2004},
     pages = {1793-1810},
     doi = {10.5802/aif.2066},
     zbl = {02162441},
     mrnumber = {2134224},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2004__54_6_1793_0}
}
Sur l'indice de certaines algèbres de Lie. Annales de l'Institut Fourier, Volume 54 (2004) no. 6, pp. 1793-1810. doi : 10.5802/aif.2066. http://www.numdam.org/item/AIF_2004__54_6_1793_0/

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