Henrik Winther

We construct an infinite family of endofunctors on the category of left modules over a unital associative algebra equipped with a differential calculus. These functors generalize the jet functors on vector bundles from differential geometry. In particular, our construction coincides with the classical jet functor for vector bundles when the algebra is the smooth functions on a manifold and the calculus is generated by the classical exterior derivative. We show that our jet functors gives rise to a category of linear differential operators between modules, that these satisfy many good properties one might expect, and that most maps which are expected to be differential operators (connections, differentials, partial derivatives) are. We also discuss representatibility, symbols and define a notion of vector fields in this setting. Joint work with K. Flood and M. Mantegazza.