A note on the Jordan decomposition
| dc.creator | Patrão, Mauro | |
| dc.creator | Santos, Laércio | |
| dc.creator | Seco, Lucas | |
| dc.date | 2008-07-29 | |
| dc.date.accessioned | 2026-07-07T09:53:33Z | |
| dc.date.available | 2026-07-07T09:53:33Z | |
| dc.description | In this article we prove that the elliptic, hyperbolic and nilpotent (or unipotent) additive (or multiplicative) Jordan components of an endomorphism $X$ (or an isomorphism $g$) of a finite dimensional vector space are given by polynomials in $X$ (or in $g$). By using this, we provide a simple proof that, for an element $X$ of a linear semisimple Lie algebra $\g$ (or $g$ of a linear semisimple connected Lie group $G$), its three Jordan components lie again in the algebra (in the group). This was previously unknown for linear Lie groups other then $\Int(\g)$. This implies that, for this class of algebras and groups, the usual linear Jordan decomposition coincides with the abstract Jordan decomposition. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/0807.4685 | |
| dc.identifier | http://arxiv.org/abs/0807.4685 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165993 | |
| dc.subject | Group Theory | |
| dc.subject | Rings and Algebras | |
| dc.title | A note on the Jordan decomposition | |
| dc.type | text |