Formula omitted]-algebra actions

Abstract

We define the notion of action of an L∞-algebra g on a graded manifold M, and show that such an action corresponds to a homological vector field on g[1]×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∞-algebra, leading to a notion of “semidirect product” of L∞-algebras more general than those we found in the literature.