A note on the Bruhat decomposition of semisimple Lie groups
Group Theory
2008-07-29 v1
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.
Cite
@article{arxiv.0807.4350,
title = {A note on the Bruhat decomposition of semisimple Lie groups},
author = {Lucas Seco},
journal= {arXiv preprint arXiv:0807.4350},
year = {2008}
}
Comments
7 pages