L-infinity algebra actions

Abstract

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.