no. 3
Surprising properties of centralisers in classical Lie algebras
[Propriétés surprenantes des centralisateurs dans les algèbres de Lie classiques]
Yakimova, Oksana1
1 Universität Erlangen-Nürnberg Mathematisches Institut Bismarckstrasse 1 1/2 91054 Erlangen (Germany)
Annales de l'Institut Fourier, Tome 59 (2009) no. 3, pp. 903-935.

Soit 𝔤 une algèbre de Lie classique, i.e., 𝔤𝔩 n , 𝔰𝔭 n , ou 𝔰𝔬 n , et soit e un élément nilpotent de 𝔤. Nous étudions dans cet article diverses propriétés du centralisateur 𝔤 e de e. Les quatre premières sections concernent des problèmes assez élémentaires portant sur le centre de 𝔤 e , la variété commutante de 𝔤 e , ou encore les centralisateurs des paires commutantes. La seconde partie aborde des questions liées aux différentes structures de Poisson sur 𝔤 e * et aux invariants symétriques de 𝔤 e .

Let 𝔤 be a classical Lie algebra, i.e., either 𝔤𝔩 n , 𝔰𝔭 n , or 𝔰𝔬 n and let e be a nilpotent element of 𝔤. We study various properties of the centralisers 𝔤 e . The first four sections deal with rather elementary questions, like the centre of 𝔤 e , commuting varieties associated with 𝔤 e , or centralisers of commuting pairs. The second half of the paper addresses problems related to different Poisson structures on 𝔤 e * and symmetric invariants of 𝔤 e .

DOI : 10.5802/aif.2451
Classification : 17B45
Keywords: Nilpotent orbits, centralisers, symmetric invariants
Mot clés : orbite nilpotente, centralisateurs, invariants symétriques

Yakimova, Oksana 1

1 Universität Erlangen-Nürnberg Mathematisches Institut Bismarckstrasse 1 1/2 91054 Erlangen (Germany) 
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Yakimova, Oksana. Surprising properties of centralisers in classical Lie algebras. Annales de l'Institut Fourier, Tome 59 (2009) no. 3, pp. 903-935. doi : 10.5802/aif.2451. https://aif.centre-mersenne.org/articles/10.5802/aif.2451/

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