On the canonical connection for smooth envelopes. (English) Zbl 1293.58002

Summary: 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 vice-versa can be done as well. In a physical language, this would correspond to the existence of a canonical connection. In this paper, we show an example of an algebra which always possesses such a connection.


58A40 Differential spaces
13N15 Derivations and commutative rings
53B05 Linear and affine connections
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