L-infinity algebras and deformation theory

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A differential graded Lie algebra is a graded -vector space endowed with a differential of degree and a bracket (of degree ), such that

is skew symmetric,
satisfies the Jacobi identity,
acts as a derivation with respect to .

We denote the cohomology of with respect to by . It is a graded vector space over , and it inherits a Lie bracket. (In fact, it is an -algebra.)