How derivation map for Differential algebra can be defined?

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A Lie λ-differential algebra is a Lie algebra L with a linear operator D : L → L satisfying the differential relation

$D([xy]) = [D(x)y] + [xD(y)] + λ[D(x)D(y)], x, y ∈ L. $

How derivation map can be defined on Lie λ-differential algebra?