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Jacobi algebras and Lie-Rinehart-Jacobi algebras. (Algèbres de Jacobi et algèbres de Lie-Rinehart-Jacobi.) (French. English summary) Zbl 1163.17025

Summary: We define the Jacobi 1-form and the Jacobi 2-form of a Jacobi algebra. We construct the Jacobi differential complex and describe Jacobi cohomology. We show that a Jacobi algebra determines a Lie-Rinehart-Jacobi algebra and that, conversely, a symplectic Lie-Rinehart-Jacobi algebra determines a Jacobi algebra structure on the base algebra.

MSC:

17B63 Poisson algebras
53D17 Poisson manifolds; Poisson groupoids and algebroids
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