In the context of Lie algebras, a derivation is a linear map that satisfies the Leibniz rule, which states that for any two elements in the Lie algebra, the derivation applied to their Lie bracket equals the derivation applied to one element multiplied by the other element, plus the first element multiplied by the derivation applied to the second element. This concept is essential as it helps us understand how structure-preserving maps behave within Lie algebras and connects to important ideas such as automorphisms and representations.
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