A Note on Derivations of Lie Algebras

Details A Note on Derivations of Lie Algebras A Note on Derivations of Lie Algebras

2010-11-07

arxiv.org/abs/1011.1609v1

Mathematics

Representation Theory

4 pages

Scientific paper

In this note, we will prove that a finite dimensional Lie algebra $L$ of
characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$
with the property $$ L^n\subseteq \sum_{d\in D}d(L) $$ for some $n\geq 1$, is
necessarily solvable. As a result, if $L$ has a derivation $d:L\to L$, such
that $L^n\subseteq d(L)$, for some $n\geq 1$, then $L$ is solvable.

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