Lie-Rinehart and Hochschild cohomology for algebras of differential operators (Q2196317)

This paper applies homological algebras techniques for Lie Rinehard algebras. First, the authors describe a spectral sequence that converges to the Hochschild cohomology of the enveloping algebra of a Lie-Rinehart algebra. Then, they consider the algebra of differential operators associated to a central arrangement of three lines. They compute the Hilbert series of the Hochschild cohomology. Examples are then studied.