Topological algebras and abstract differential geometry
type: Item
instance of: scholarly article
title: Topological algebras and abstract differential geometry
zbMATH Open document ID: 0936.53022
DOI: 10.1007/BF02169286
author: Yanyan Li
published in: Journal of Mathematical Sciences (New York)
publication date: 2000-01-25T00:00:00Z
review text: The notions of connection and curvature on principal sheaves, with structural sheaf the sheaf of groups \({\mathcal G}{\mathcal L}(n, {\mathcal A})\), are studied where \({\mathcal A}\) is a sheaf of unital, commutative and associative algebras. Suitable topological algebras provide concrete models of principal sheaves for which an abstract Frobenius integrability condition holds, thus establishing the equivalence between flatness, parallelism and integrability of a connection on them. Some forthcoming papers of the author on this theory are announced.
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 55R65
Mathematics Subject Classification ID: 58A40
Mathematics Subject Classification ID: 46M20
zbMATH DE Number: 1393015
zbMATH Keywords: differential triad of an algebra
zbMATH Keywords: connection on a principal sheaf
zbMATH Keywords: curvature of a connection
zbMATH Keywords: Frobenius theorem
Wikidata QID: Q115392732
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
cites work: Q3938903
cites work: Q5655596
cites work: Q5547767
cites work: Q5731354
cites work: Q3730448
cites work: Q4296697
cites work: The de Rham-Kähler complex of the Gel'fand sheaf of a topological algebra
cites work: On an axiomatic approach to geometric prequantization: a classification scheme à la Kostant-Souriau-Kirillov
cites work: The differentiable space structures of Milnor classifying spaces, simplicial complexes, and geometric realizations
cites work: Q4357620
cites work: ON A GENERALIZATION OF THE NOTION OF MANIFOLD
cites work: Differential modules
cites work: The de Rham theorem for general spaces
cites work: Q4349028
cites work: Q4263202
cites work: Q5691176
cites work: Q4385669
description: scientific article; zbMATH DE number 1393015