Superdistributions
type: Item
instance of: scholarly article
title: Superdistributions
zbMATH Open document ID: 0652.58013
DOI: 10.1007/BF00416567
author: S. Nagamachi
author: Yuji Kobayashi
published in: Letters in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: The standard definition of generalized functions (distributions) is generalized to supermanifolds in the frameworks developed in earlier papers of the authors. Having overcome technical obstructions, the authors get a result well-known and obvious if another definition of supermanifold is used (as of a ringed space): since the superspace of functions on a supermanifold is locally the tensor product of the algebra of functions on the underlying space by a finite-dimensional space (Grassmann algebra) V, its dual is the tensor product of the space of distributions on the underlying space by \(V^*\). (The authors in addition identify V with \(V^*\), uncanonically in general case, with the help of Berezin integral over odd variables.)
Mathematics Subject Classification ID: 58C50
zbMATH DE Number: 4064092
zbMATH Keywords: distributions
zbMATH Keywords: supermanifolds
zbMATH Keywords: superspace of functions
reviewed by: Dimitry Leites
MaRDI profile type: Publication
cites work: A global theory of supermanifolds
cites work: Analysis on generalized superspaces
cites work: Generalized complex superspace—Involutions of superfields
cites work: Usage of infinite-dimensional nuclear algebras in superanalysis
full work available at URL: https://doi.org/10.1007/bf00416567
OpenAlex ID: W4241279558
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description: scientific article; zbMATH DE number 4064092