A representation formula for maps on supermanifolds

@article{Hlein2008ARF,
  title={A representation formula for maps on supermanifolds},
  author={Fr{\'e}d{\'e}ric H{\'e}lein},
  journal={Journal of Mathematical Physics},
  year={2008},
  volume={49},
  pages={023506}
}
  • F. Hélein
  • Published 17 March 2006
  • Mathematics
  • Journal of Mathematical Physics
We analyze the notion of morphisms of rings of superfunctions which is the basic concept underlying the definition of supermanifolds as ringed spaces (i.e., following Berezin, Leites, Manin, etc.). We establish a representation formula for all (pull-back) morphisms from the algebra of functions on an ordinary manifolds to the superalgebra of functions on an open subset of a superspace. We then derive two consequences of this result. The first one is that we can integrate the data associated… 

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References

SHOWING 1-10 OF 20 REFERENCES

Two approaches to supermanifolds

The problem of supplying an analogue of a manifold whose sheaf of functions contains anticommuting elements has been approached in two ways. Either one extends the sheaf of functions formally, as in

Introduction to Superanalysis

1. Grassmann Algebra.- 2. Superanalysis.- 3. Linear Algebra in Z2-Graded Spaces.- 4. Supermanifolds in General.- 5. Lie Superalgebras.- 1. Lie Superalgebras.- 2. Lie Supergroups.- 3. Laplace-Casimir

A Global Theory of Supermanifolds

A mathematically rigorous definition of a global supermanifold is given. This forms an appropriate model for a global version of superspace, and a class of functions is defined which corresponds to

Introduction to the Theory of Supermanifolds

CONTENTSIntroduction Chapter I. Linear algebra in superspaces § 1. Linear superspaces § 2. Modules over superalgebras § 3. Matrix algebra § 4. Free modules § 5. Bilinear forms § 6. The supertrace §

Super Lie groups: global topology and local structure

A general mathematical framework for the super Lie groups of supersymmetric theories is presented. The definition of super Lie group is given in terms of supermanifolds, and two theorems (analogous

Gauge Field Theory and Complex Geometry

Geometrical Structures in Field Theory.- 1. Grassmannians, Connections, and Integrability.- 2. The Radon-Penrose Transform.- 3. Introduction to Superalgebra.- 4. Introduction to Supergeometry.- 5.

Supersymmetry for Mathematicians: An Introduction

Introduction The concept of a supermanifold Super linear algebra Elementary theory of supermanifolds Clifford algebras, spin groups, and spin representations Fine structure of spin modules

Introduction to Supersymmetry: Cambridge Monographs on Mathematical Physics

Peter G 0 Freund 1986 Cambridge: Cambridge University Press x + 152 pp price £20 ISBN 0 521 26880X The success of gauge theories as a solution to the problem of interacting relativistic quantum

Quantum Fields and Strings: A Course for Mathematicians

Ideas from quantum field theory and string theory have had considerable impact on mathematics over the past 20 years. Advances in many different areas have been inspired by insights from physics. In

The Geometry Of Schemes

1 Basic Definitions 2 Examples 3 Projective Schemes 4 Classical Constructions 5 Local Constructions 6 Schemes and Functors