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arXiv · 0807.4350

A note on the Bruhat decomposition of semisimple Lie groups

Lucas Seco
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Abstract

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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Lucas Seco. 2008-07-28. A note on the Bruhat decomposition of semisimple Lie groups. https://arxiv.org/abs/0807.4350

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