Crossed modules for Lie–Rinehart algebras

We introduce the notion of crossed module for Lie–Rinehart algebras and prove that they are classified by the third cohomology of Lie–Rinehart algebras developed in [J. Huebschmann, J. Reine Angew. Math. 408 (1990) 57–113; G.S. Rinehart, Trans. Amer. Math. Soc. 108 (1963) 195–222].