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.

v2: Final version, to appear in Diff. Geom. Appl

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Cited by in corpus (11)

• Representations of Homotopy Lie-Rinehart Algebras
• Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
• Nonabelian higher derived brackets
• Algebraic models of local period maps and Yukawa algebras
• Higher Lie algebra actions on Lie algebroids
• Distributions and quotients on degree 1 NQ-manifolds and Lie algebroids
• Homotopy relative Rota-Baxter Lie algebras, triangular $L_{\infty }$-bialgebras and higher derived brackets
• Connections Adapted to Non-Negatively Graded Structures
• Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids
• Homotopy theory of curved operads and curved algebras
• $L_{\infty }$-actions of Lie algebroids