Products and vector bundles within the category of \(G\)-supermanifolds
type: Item
instance of: scholarly article
title: Products and vector bundles within the category of \(G\)-supermanifolds
zbMATH Open document ID: 0843.58003
DOI: 10.1007/BF00971235
author: Claudio Bartocci
author: Ugo Bruzzo
author: Daniel Hernandez Ruiperez
published in: Siberian Mathematical Journal
publication date: 1995-12-12T00:00:00Z
review text: Let \((M, A)\) be a supermanifold over the basic algebra \(B\) (graded commutative Banach algebra), where \(M\) is an underlying topological manifold and \(A\) is a sheaf of supercommutative \(B\)-algebras. It is known that \(A\) under some reasonable conditions is not a sheaf of functions. Therefore, many of the usual geometric constructions such as the products and vector bundles are not so immediate as in the usual differential geometry. The authors develop the concepts of a product of \(G\)-supermanifolds and (super)vector bundles in the spirit of Berezin-Leites-Konstant.
Mathematics Subject Classification ID: 58A50
zbMATH DE Number: 825529
zbMATH Keywords: supermanifold
zbMATH Keywords: products
zbMATH Keywords: vector bundles
reviewed by: Valery Borisovich Marenich
MaRDI profile type: Publication
cites work: Q3697706
cites work: The Axioms of Supermanifolds and a New Structure Arising From Them
cites work: Some remarks on the differential-geometric approach to supermanifolds
cites work: Q4130629
cites work: Global variational calculus on graded manifolds. I: Graded jet bundles, structure 1-form and graded infinitesimal contact transformations
cites work: Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras
cites work: Two Approaches to Supermanifolds
cites work: A global theory of supermanifolds
cites work: Q5731354
full work available at URL: https://doi.org/10.1007/bf00971235
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description: scientific article; zbMATH DE number 825529