A Note on Derivations of Lie Algebras

Mohammad Shahryari

Abstract


In this note, we will prove that a finite dimensional Lie algebra $L$ over an algebraically closed field 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 $n>1$, is necessarily solvable. As a result, we show that, if $L$ has a derivation $d:L\to L$, such that $L^n\subseteq d(L)$, for some $n>1$, then $L$ is solvable.

doi:10.1017/S0004972711002516

Keywords


Lie algebras, Derivations, Solvable Lie algebras, Compact Lie groups



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