Jordan–Chevalley Decomposition in Lie Algebras
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Published:2019-02-28
Issue:02
Volume:62
Page:349-354
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ISSN:0008-4395
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Container-title:Canadian Mathematical Bulletin
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language:en
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Short-container-title:Can. Math. Bull.
Author:
Cagliero Leandro,Szechtman Fernando
Abstract
AbstractWe 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
$A=S+N$
.
Publisher
Canadian Mathematical Society
Subject
General Mathematics