Differential Geometry and its Application
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×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.
Action, Extension, Graded manifold, L -algebra ∞, Lie algebroid
Mehta, Rajan Amit and Zambon, Marco, "L ∞-Algebra Actions" (2012). Mathematics and Statistics: Faculty Publications, Smith College, Northampton, MA.