A representation formula for maps on supermanifolds

  title={A representation formula for maps on supermanifolds},
  author={Fr{\'e}d{\'e}ric H{\'e}lein},
  journal={Journal of Mathematical Physics},
  • 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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