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

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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 
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/JOLT_2008_18_3_a14/
@article{JOLT_2008_18_3_a14,
     author = {L. Seco},
     title = {A {Note} on the {Bruhat} {Decomposition} of {Semisimple} {Lie} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {725--731},
     year = {2008},
     volume = {18},
     number = {3},
     zbl = {1228.22016},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2008_18_3_a14/}
}
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