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Algebra and Discrete Mathematics, 2009, Issue 1, Pages 74–82
(Mi adm109)
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This article is cited in 5 scientific papers (total in 5 papers)
RESEARCH ARTICLE
On action of outer derivations on nilpotent ideals of Lie algebras
Dmitriy V. Maksimenko Kiev Taras Shevchenko University, Faculty of Mechanics and Mathematics, 64, Volodymyrska street, 01033 Kyiv,
Ukraine
Abstract:
Action of outer derivations on nilpotent ideals of Lie algebras are considered. It is shown that for a nilpotent ideal $I$ of a Lie algebra $L$ over a field $F$ the ideal $I+D(I)$ is nilpotent, provided that $char F=0$ or $I$ nilpotent of nilpotency class less than $p-1$, where $p=char F$. In particular, the sum $N(L)$ of all nilpotent ideals of a Lie algebra $L$ is a characteristic ideal, if $char F=0$ or $N(L)$ is nilpotent of class less than $p-1$, where $p=char F$.
Keywords:
Lie algebra, derivation, solvable radical, nilpotent ideal.
Received: 24.09.2007 Revised: 14.04.2009
Citation:
Dmitriy V. Maksimenko, “On action of outer derivations on nilpotent ideals of Lie algebras”, Algebra Discrete Math., 2009, no. 1, 74–82
Linking options:
https://www.mathnet.ru/eng/adm109 https://www.mathnet.ru/eng/adm/y2009/i1/p74
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Abstract page: | 187 | Full-text PDF : | 109 | First page: | 1 |
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