Journal of Lie Theory 18 (2008), No. 3, 725--731
Copyright Heldermann Verlag 2008
A Note on the Bruhat Decomposition of Semisimple Lie Groups
Lucas Seco
Instituto de Matemática, Universidade Estadual de Campinas, Cx. Postal 6065 / 13.081-970, Campinas - SP, Brasil
lseco@ime.unicamp.br
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.
Keywords: Bruhat decomposition, flag manifold.
MSC: 22E46; 14M15
[ Fulltext-pdf (143 KB)] for subscribers only.