Journal of Lie Theory

no. 3
A Note on the Bruhat Decomposition of Semisimple Lie Groups
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 725-731
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.
DOI: 10.5802/jolt.521
Classification: 22E46, 14M15
Keywords: Bruhat decomposition, flag manifold 
@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},
     doi = {10.5802/jolt.521},
     zbl = {1228.22016},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.521/}
}
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L. Seco. A Note on the Bruhat Decomposition of Semisimple Lie Groups. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 725-731. doi: 10.5802/jolt.521

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