This article is cited 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.

MSC: 17B40

Received: 24.09.2007
Revised: 14.04.2009

Language: English

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