2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165882Let 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.7 pagesGroup Theory22E46; 14M15text