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Leandro, Cagliero; Szechtman, Fernando
Jordan-Chevalley decomposition in Lie algebras
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 $A=S+N$.

Keywords:solvable Lie algebra, Jordan-Chevalley decomposition, representation
Categories:17-08, 17B05, 20C40, 15A21

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