On the canonical connection for smooth envelopes

A notion known as smooth envelope, or superposition closure, appears naturally in several approaches to generalized smooth manifolds which were proposed in the last decades. Such an operation is indispensable in order to perform differential calculus. A derivation of the enveloping algebra can be restricted to the original one, but it is a delicate question if the the vice-versa can be done as well. In a physical language, this would corresponds to the existence of a canonical connection. In this paper we show an example of an algebra which always possesses such a connection.