Differential operators on projective modules

Helge Maakestad

Published 2011-10-22, updated 2012-10-23Version 9

In this paper we give explicit formulas for differential operators on a finitely generated projective module E on an arbitrary commutative unital ring A. We use the differential operators constructed to give a simple formula for the curvature of a connection on a Lie-Rinehart algebra in terms of the fundamental matrix of E. This gives an explicit formula for the curvature of a connection on E defined in terms of an idempotent for E. We also consider the notion of a stratification on the module E induced by a projective basis. It turns out few stratifications are induced by a projective basis.