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

Voir la notice de l'article provenant de la source Cambridge University Press

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
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2018-023-7/}
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[B1] Bourbaki, N., Lie Groups and Lie Algebras: chapters 1–3. Springer-Verlag, Berlin, 1989. Google Scholar

[B2] Bourbaki, N., Lie Groups and Lie Algebras: chapters 7–9. Springer-Verlag, Berlin, 2005. Google Scholar

[CS] Cagliero, L. and Szechtman, F., Jordan–Chevalley decomposition in finite dimensional Lie algebras . Proc. Amer. Math. Soc. 139(2011), no. 11, 3909–3913. . Google Scholar | DOI

[CS2] Cagliero, L. and Szechtman, F., The classification of uniserial -modules and a new interpretation of the Racah–Wigner 6j-symbol. J. Algebra (2013), 142–175. . Google Scholar | DOI

[CS3] Cagliero, L. and Szechtman, F., On the theorem of the primitive element with applications to the representation theory of associative and Lie Algebras . Canad. Math. Bull. 57(2014), no. 4, 735–748. . Google Scholar | DOI

[FH] Fulton, W. and Harris, J., Representation theory: A first course. Graduate Texts in Mathematics, 129, Readings in Mathematics, Springer-Verlag, New York, 1991. . Google Scholar | DOI

[HK] Hoffman, K. and Kunze, R., Linear algebra. Second ed., Prentice-Hall, New Jersey, 1971. Google Scholar

[Hu] Humphreys, J. E., Introduction to Lie algebras and representation theory. Graduate Texts in Mathematics, 9, Springer-Verlag, New York-Berlin, 1978. Google Scholar

[Ki] Kim, K.-T., Criteria for the existence of a Jordan–Chevalley-Seligman decomposition . J. Algebra 424(2015), 376–389. . Google Scholar | DOI

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