A note on the Bruhat decomposition of semisimple Lie groups

2008/07/28 by Lucas Seco, Seco, Lucas
Mathematics · #14M15 #22E46 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:14M15 #msc:22E46

paper · pdf · doi:10.48550/arxiv.0807.4350

7 pages

arxiv created 2008/07/28 · arxiv updated 2009/12/01

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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