The Chevalley-Eilenberg complex is usually defined a bit more generally for Lie algebras equipped with a Lie module? . In the above language this more general cochain complex is the one underlying the Lie ∞-algebroid that encodes this action in the sense of Lie ∞-algebroid representations.
Lie algebra cohomology
The cohomology of the Chevalley-Eilenberg cochain complex agrees with the Lie algebra cohomology with trivial coefficients. The Lie algebra is however defined also for infinite-dimensional Lie algebras and arbitrary module coefficients. Namely the Lie algebra cohomology is where is the universal enveloping of and (with the appropriate differential) is the Chevalley-Eilenberg chain complex. Now if is finite-dimensional then and .