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Representations of Homotopy Lie–Rinehart Algebras

Published online by Cambridge University Press:  04 December 2014

DipMat, Università degli Studi di Salerno, & Istituto Nazionale di Fisica Nucleare, GC Salerno, Via Giovanni Paolo II n° 123, 84084 Fisciano (SA), Italy. e-mail:
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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 algebras on graded manifolds. I also discuss the Schouten-Nijenhuis calculus associated to strong homotopy Lie–Rinehart connections.

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