Derivations and local derivations on Euclidean Lie algebras

Abstract

The present paper is devoted to studying derivations and local derivations on the Euclidean Lie algebras $\mathfrak{e}(n)$. We give a complete desrciption of the derivation algebra of $\mathfrak{e}(n)$ for $n\ge 4$. Furthermore, we prove that every local derivations on the $\mathfrak{e}(n)$ is a derivation.