nLab derivation Lie 2-algebra

Definition

For $\mathfrak{g}$ a Lie algebra, its derivation Lie 2-algebra is the corresponding automorphism ∞-Lie algebra:

it is the strict Lie 2-algebra coming from the differential crossed module that is given by the chain complex

$$\partial : \mathfrak{g} \stackrel{Ad}{\to} Der(\mathfrak{g})$$

equipped with the canonical Lie action of the derivation Lie algebra $Der(\mathfrak{g})$ on $\mathfrak{g}$.