  We define the notion of action of an L-infinity algebra $g$ on a graded
manifold $M$, and show that such an action corresponds to a homological vector
field on $g[1] \times M$ of a specific form. This generalizes the
correspondence between Lie algebra actions on manifolds and transformation Lie
algebroids. In particular, we consider actions of $g$ on a second L-infinity
algebra, leading to a notion of "semidirect product" of L-infinity algebras
more general than those we found in the literature.
