L-infinity algebra actions

Rajan Mehta; Marco Zambon

doi:10.1016/j.difgeo.2012.07.006

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arXiv · 1202.2607

L-infinity algebra actions

Rajan Mehta·Marco Zambon

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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.

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Rajan Mehta, Marco Zambon. 2012-08-30. L-infinity algebra actions. https://doi.org/10.1016/j.difgeo.2012.07.006

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