On the Canonical Connection for Smooth Envelopes

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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Main Author: Moreno Giovanni
Format: Article
Language:English
Published: De Gruyter 2014-06-01
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
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spelling doaj-b61dfa6739494b35847245867edfa5e32020-11-25T01:14:09ZengDe GruyterDemonstratio Mathematica0420-12132391-46612014-06-0147245946410.2478/dema-2014-0036dema-2014-0036On the Canonical Connection for Smooth EnvelopesMoreno Giovanni0MATHEMATICAL INSTITUTE IN OPAVA SILESIAN UNIVERSITY IN OPAVA Na Rybnicku 626/1 746 01 OPAVA, CZECH REPUBLICA 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.http://www.degruyter.com/view/j/dema.2014.47.issue-2/dema-2014-0036/dema-2014-0036.xml?format=INT
collection DOAJ
language English
format Article
sources DOAJ
author Moreno Giovanni
spellingShingle Moreno Giovanni
On the Canonical Connection for Smooth Envelopes
Demonstratio Mathematica
author_facet Moreno Giovanni
author_sort Moreno Giovanni
title On the Canonical Connection for Smooth Envelopes
title_short On the Canonical Connection for Smooth Envelopes
title_full On the Canonical Connection for Smooth Envelopes
title_fullStr On the Canonical Connection for Smooth Envelopes
title_full_unstemmed On the Canonical Connection for Smooth Envelopes
title_sort on the canonical connection for smooth envelopes
publisher De Gruyter
series Demonstratio Mathematica
issn 0420-1213
2391-4661
publishDate 2014-06-01
description 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.
url http://www.degruyter.com/view/j/dema.2014.47.issue-2/dema-2014-0036/dema-2014-0036.xml?format=INT
work_keys_str_mv AT morenogiovanni onthecanonicalconnectionforsmoothenvelopes
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