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Prove that the composition of Lie algebra derivations need not be a derivation. [duplicate]
In case the definition is not standard, my book defines a derivation $D \in \text{End}(\mathfrak{g})$ of a Lie algebra $\mathfrak{g}$ as a linear map such that:
$D([X,Y]) = [D(X), Y]\ +\ [X, D(Y)]$ ...
