Geodesic
A Note on the Bruhat Decomposition of Semisimple Lie Groups
Journal of Lie theory, Tome 18 (2008) no. 3, pp. 725-731.

Voir la notice de l'article provenant de la source Heldermann Verlag

Let a split element of a connected semisimple Lie group act on one of its flag manifolds. We prove that each connected set of fixed points of this action is itself a flag manifold. With this we can obtain a generalized Bruhat decomposition of a semisimple Lie group by entirely dynamical arguments.
Classification : 22E46, 14M15
Mots-clés : Bruhat decomposition, flag manifold 
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     author = {L. Seco },
     title = {A {Note} on the {Bruhat} {Decomposition} of {Semisimple} {Lie} {Groups}},
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L. Seco . A Note on the Bruhat Decomposition of Semisimple Lie Groups. Journal of Lie theory, Tome 18 (2008) no. 3, pp. 725-731. http://geodesic.mathdoc.fr/item/JLT_2008_18_3_JLT_2008_18_3_a14/