
Journal of Lie Theory 18 (2008), No. 3, 725731 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 / 13.081970, 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 [ Fulltextpdf (143 KB)] for subscribers only. 