A note on the jordan decomposition
The multiplicative Jordan decomposition of a linear isomorphism of Rn 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...
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Universidad Católica del Norte, Departamento de Matemáticas
2011
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oai:scielo:S0716-091720110001000112018-10-30A note on the jordan decompositionPatrão,MauroSantos,LaércioSeco,LucasThe multiplicative Jordan decomposition of a linear isomorphism of Rn 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 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.30 n.1 20112011-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000100011en10.4067/S0716-09172011000100011 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| description |
The multiplicative Jordan decomposition of a linear isomorphism of Rn 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 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. |
| author |
Patrão,Mauro Santos,Laércio Seco,Lucas |
| spellingShingle |
Patrão,Mauro Santos,Laércio Seco,Lucas A note on the jordan decomposition |
| author_facet |
Patrão,Mauro Santos,Laércio Seco,Lucas |
| author_sort |
Patrão,Mauro |
| title |
A note on the jordan decomposition |
| title_short |
A note on the jordan decomposition |
| title_full |
A note on the jordan decomposition |
| title_fullStr |
A note on the jordan decomposition |
| title_full_unstemmed |
A note on the jordan decomposition |
| title_sort |
note on the jordan decomposition |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2011 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172011000100011 |
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