Infinitesimal natural and gauge-natural lifts
type: Item
instance of: scholarly article
title: Infinitesimal natural and gauge-natural lifts
zbMATH Open document ID: 0780.53023
DOI: 10.1016/0926-2245(92)90028-L
author: Josef Janyška
author: Marco Modugno
published in: Differential Geometry and its Applications
publication date: 1994-02-02T00:00:00Z
review text: A natural bundle functor is defined as a prolongation functor from the category of manifolds into the category of bundles, which preserves the inclusions [\textit{A. Nijenhuis}, Differential Geometry, in Honor of Kentaro Yano, 317-334 (1972; Zbl 0246.53018)]. A gauge-natural bundle functor is defined to be a prolongation functor from the category of \(G\)- principal bundles to the category of fibred manifolds, which preserves embeddings and inclusions [\textit{D. J. Eck}, Mem. Am. Math. Soc. 247 (1981; Zbl 0493.53052)]. This paper is aimed at expressing naturality and gauge-naturality at infinitesimal level, by using the concept of strong systems of vector fields [\textit{M. Modugno}, Differential geometric methods in mathematical physics, Proc. 14th Int. Conf., Salamanca/Spain 1985, Lect. Notes Math. 1251, 236-264 (1987; Zbl 0614.53072)]. The main idea is to replace the action of a Lie group with the action of a Lie algebra of vector fields. The exposition involves largely jet techniques.
reviewed by: Marco Modugno
Mathematics Subject Classification ID: 53B99
Mathematics Subject Classification ID: 58A20
zbMATH DE Number: 205000
zbMATH Keywords: natural bundle functor
zbMATH Keywords: gauge-natural bundle functor
zbMATH Keywords: strong systems of vector fields
Wikidata QID: Q115362744
MaRDI profile type: Publication
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full work available at URL: 0926-2245(92)90028-l
OpenAlex ID: W1988756071
description: scientific article; zbMATH DE number 205000