Lie-Rinehart and Poisson algebras over $C^{\infty }$-rings

Eugene Lerman, Ruben Louis

We define the analogue of Lie-Rinehart algebras over $C^{\infty }$-rings. We show that given a Poisson $C^{\infty }$-ring $\mathcal{A}$ its module ${\Omega }_{\mathcal{A}}^1$ of $C^{\infty }$-Käh…