Mappings of supermanifolds
type: Item
instance of: scholarly article
title: Mappings of supermanifolds
zbMATH Open document ID: 0569.58005
DOI: 10.1007/BF01018249
published in: Theoretical and Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: The paper concerns the paper of \textit{A. S. Shvarts} [ibid. 60, No.1, 37- 42 (1984)], where the concept of superspaces, supermanifolds etc., based on Grassmann algebras and more convenient for physics applications than the standard concept based on sheaf theory, was developed. The author proves that the concept of a smooth mapping between (p,q)-dimensional supermanifolds, defined in the sense of Shvarts, is identical to the concept of a morphism of supermanifolds in the standard approach and hence, the Shvarts' definition of a (p,q)-dimensional supermanifold is equivalent to the standard one. Theorem 1. The smooth mappings of \({\mathbb{R}}^{p,q}\) into \({\mathbb{R}}^{p',q'}\) are in a one-to-one correspondence with the parity- preserving homomorphisms of the Berezin algebra \(B^{B',q'}\) into the algebra \(B^{p,q}\). - A similar correspondence is constructed even for non-smooth mappings.
reviewed by: J.Durdil
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 15A90
zbMATH DE Number: 3909372
zbMATH Keywords: smooth mapping
zbMATH Keywords: superspaces
zbMATH Keywords: supermanifolds
zbMATH Keywords: Grassmann algebras
zbMATH Keywords: Berezin algebra
zbMATH Keywords: non-smooth mappings
author: Alexander A. Voronov
MaRDI profile type: Publication
cites work: Supergravity, complex geometry and G-structures
cites work: Q3043319
description: scientific article; zbMATH DE number 3909372