L-infinity algebras and deformation theory

A differential graded Lie algebra is a graded $$k$$-vector space $$\mathfrak{g}$$ endowed with a differential $$d:\mathfrak{g}\to\mathfrak{g}$$ of degree $$+1$$ and a bracket $$[\,]:\mathfrak{g}\otimes\mathfrak{g}\longrightarrow\mathfrak{g}$$ (of degree $$0$$), such that
 * $$[\,]$$ is skew symmetric,
 * $$[\,]$$ satisfies the Jacobi identity,
 * $$d$$ acts as a derivation with respect to $$[\,]$$.

We denote the cohomology of $$\mathfrak{g}$$ with respect to $$d$$ by $$h^*(\mathfrak{g})$$. It is a graded vector space over $$k$$, and it inherits a Lie bracket. (In fact, it is an $$L_\infty$$-algebra.)