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 r...
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| Format: | Article |
| Language: | English |
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De Gruyter
2014-06-01
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| Series: | Demonstratio Mathematica |
| Online Access: | http://www.degruyter.com/view/j/dema.2014.47.issue-2/dema-2014-0036/dema-2014-0036.xml?format=INT |
| 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 the viceversa 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. |
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| ISSN: | 0420-1213 2391-4661 |