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Jordan-Chevalley decomposition in Lie algebras
2018
Canadian mathematical bulletin
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We prove that if s is a solvable Lie algebra of matrices over a eld of characteristic and A ∈ s, then the semisimple and nilpotent summands of the Jordan-Chevalley decomposition of A belong to s if and only if there exist S, N ∈ s, S is semisimple, N is nilpotent (not necessarily [S, N] = ) such that A = S + N.
doi:10.4153/cmb-2018-023-7
fatcat:pqsij3hwtnh2dlvudnmqgfmasu