A note on the jordan decomposition

Mauro Patrão, Laércio Santos, Lucas Seco
2011 Proyecciones  
The multiplicative Jordan decomposition of a linear isomorphism of R n into its elliptic, hyperbolic and unipotent components is well know. One can define an abstract Jordan decomposition of an element of a Lie group by taking the Jordan decomposition of its adjoint map. For real algebraic Lie groups, some results of Mostow implies that the usual multiplicative Jordan decomposition coincides with the abstract Jordan decomposition. Here, for a semisimple linear Lie group, we obtain this fact by
more » ... btain this fact by elementary methods. We also obtain the corresponding results for semisimple linear Lie algebras. Complete and simple proofs of these facts are lacking in the literature, so that the main purpose of this article is to fill this gap.
doi:10.4067/s0716-09172011000100011 fatcat:bnumfhbasjb4xksrznoutytqeu