nLab
derivation Lie 2-algebra

Definition

For $𝔤$ 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

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

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