Chevalley-Eilenberg cohomology of (graded) Lie algebras over . Mentioned here.
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[arXiv:1109.3715]http://front.math.ucdavis.edu/1109.3715) Maurer-Cartan moduli and models for function spaces from arXiv Front: math.AT by Andrey Lazarev We set up a formalism of Maurer-Cartan moduli sets for L-infinity algebras and associated twistings based on the closed model category structure on formal differential graded algebras (a.k.a. differential graded coalgebras). Among other things this formalism allows us to give a compact and manifestly homotopy invariant treatment of Chevalley-Eilenberg and Harrison cohomology. We apply the developed technology to construct rational homotopy models for function spaces.
Notes introducing the Chevalley-Eilenberg cohomology of a Lie algebra
nLab page on Chevalley-Eilenberg cohomology