A note on the Bruhat decomposition of semisimple Lie groups

Details A note on the Bruhat decomposition of semisimple Lie groups A note on the Bruhat decomposition of semisimple Lie groups

2008-07-28

arxiv.org/abs/0807.4350v1

Mathematics

Group Theory

7 pages

Scientific paper

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 the generalized Bruhat
decomposition of a semisimple Lie group by entirely dynamical arguments.

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