We prove that δ-derivations of a simple finite-dimensional Lie algebra over a field of characteristic zero, with values in a finite-dimensional module, are either inner derivations, or, in the case of adjoint module, multiplications by a scalar, or some exceptional cases related to $\mathfrak{sl}(2)$. This can be viewed as an extension of the classical first Whitehead Lemma.

中文翻译：

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一个δ -第一白石引理

我们证明在特征零域上具有有限维模块中的值的简单有限维李代数的δ导数是内部导数，或者在伴随模数的情况下，是标量的乘积，或者一些与$\mathfrak{sl}（2）$。这可以看作是经典的第一个Whitehead Lemma的扩展。