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Representations of homotopy Lie-Rinehart algebras. (English) Zbl 1371.17018

Summary: I propose a definition of left/right connection along a strong homotopy Lie-Rinehart algebra. This allows me to generalise simultaneously representations up to homotopy of Lie algebroids and actions of \(L_\infty\) algebras on graded manifolds. I also discuss the Schouten-Nijenhuis calculus associated to strong homotopy Lie-Rinehart connections.

MSC:

17B55 Homological methods in Lie (super)algebras
53D17 Poisson manifolds; Poisson groupoids and algebroids
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