Geodesic
Jordan–Chevalley Decomposition in Lie Algebras
Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 349-354

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DOI

We prove that if $\mathfrak{s}$ is a solvable Lie algebra of matrices over a field of characteristic 0 and $A\in \mathfrak{s}$, then the semisimple and nilpotent summands of the Jordan–Chevalley decomposition of $A$ belong to $\mathfrak{s}$ if and only if there exist $S,N\in \mathfrak{s}$, $S$ is semisimple, $N$ is nilpotent (not necessarily $[S,N]=0$) such that $A=S+N$.
DOI : 10.4153/CMB-2018-023-7
Mots-clés : solvable Lie algebra, Jordan–Chevalley decomposition, representation 
Cagliero, Leandro; Szechtman, Fernando. Jordan–Chevalley Decomposition in Lie Algebras. Canadian mathematical bulletin, Tome 62 (2019) no. 2, pp. 349-354. doi: 10.4153/CMB-2018-023-7
@article{10_4153_CMB_2018_023_7,
     author = {Cagliero, Leandro and Szechtman, Fernando},
     title = {Jordan{\textendash}Chevalley {Decomposition} in {Lie} {Algebras}},
     journal = {Canadian mathematical bulletin},
     pages = {349--354},
     year = {2019},
     volume = {62},
     number = {2},
     doi = {10.4153/CMB-2018-023-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-023-7/}
}
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