2006/03/17 by Frédéric Hélein · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebra over a field #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Morphism #Representation (politics) #Simple (philosophy) #Superalgebra #Supermanifold #Uniqueness #hep-th #math-ph #math.DG #math.MP #msc:14A10 #msc:53Z05 #msc:58A50
paper · pdf · doi:10.1063/1.2840464
published as J.Math.Phys.49:023506,2008 · 23 pages
arxiv created 2006/03/17 · openalex publication_date 2008/02/01 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 with a morphism in order to get a (nonunique) map defined on an ordinary space (and uniqueness can be achieved by restriction to a scheme). The second one is a simple and intuitive recipe to compute pull-back images of a function on a manifold M by a map from a superspace to M.