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Lie algebras are algebraic structures which were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" (after Sophus Lie) was introduced by Hermann Weyl in the 1930s. In older texts, the name "infinitesimal group" is used. Related mathematical concepts include Lie groups and differentiable manifolds.
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An identity in Lie algebras over fields of positive characteristic
Yes, this identity holds, and both sides are equal to $-D^p(x^p)$.
We need the following facts, all of which are straightforward to verify, where $D$ is an arbitrary derivation, still working over ch …