On a `super' version of Lie's third fundamental theorem
type: Item
instance of: scholarly article
title: On a `super' version of Lie's third fundamental theorem
zbMATH Open document ID: 0692.22010
DOI: 10.1007/BF00397054
published in: Letters in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: Let A be a topological algebra, \(A^ 0\) its dual coalgebra and \(\hat A\) be the subset of \(A^ 0\) consisting of all continuous functionals. A is said to obey duality, if it is Hausdorff and the polars of all equicontinuous subfamilies of \(\hat A\) taken with respect to the pairing \((A,\hat A)\) form a neighborhood basis of zero in A. It is proved that any finite-dimensional super Lie module W, over a graded-commutative Banach algebra B obeying duality is enlargeable.
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 46S20
Mathematics Subject Classification ID: 58C50
Mathematics Subject Classification ID: 17A70
Mathematics Subject Classification ID: 46H25
Mathematics Subject Classification ID: 16W30
zbMATH DE Number: 4132479
zbMATH Keywords: topological algebra
zbMATH Keywords: dual coalgebra
zbMATH Keywords: continuous functionals
zbMATH Keywords: obey duality
zbMATH Keywords: polars
zbMATH Keywords: equicontinuous subfamilies
zbMATH Keywords: finite-dimensional super Lie module
zbMATH Keywords: graded-commutative Banach algebra
author: Vladimir G. Pestov
reviewed by: Melih Boral
MaRDI profile type: Publication
cites work: A global theory of supermanifolds
cites work: Super Lie groups: global topology and local structure
cites work: Superspaces and supersymmetries
cites work: Graded manifolds, supermanifolds and infinite-dimensional Grassmann algebras
cites work: Cohomology of the structure sheaf of real and complex supermanifolds
cites work: Supergravity, complex geometry and G-structures
cites work: An existence result for super Lie groups
cites work: Enlargeable graded Lie algebras of supersymmetry
cites work: Q5562589
cites work: Chern–Simons forms on principal superfiber bundles
cites work: Usage of infinite-dimensional nuclear algebras in superanalysis
cites work: On the structure of superfields in a field theory on a supermanifold
full work available at URL: https://doi.org/10.1007/bf00397054
OpenAlex ID: W2089700977
description: scientific article; zbMATH DE number 4132479