The diffeomorphism supergroup of a finite-dimensional supermanifold. (English) Zbl 1268.58009

The authors focus on the definition and basic properties of the diffeomorphism supergroup of a supermanifold. The first part of the paper is devoted to a self-contained overview of super geometry in the categorical approach.
Then they define and study the concept of morphisms of supermanifolds in this approach. The invertible morphisms can be seen to possess a supergroup structure. An essential result is a structure theorem providing a factorization of this supergroup. Using this, analytic difficulties can be reduced to the underlying manifold.
The main result of the paper is a proof that the supergroup of diffeomorphisms is in fact a Fréchet Lie supergroup.


58C50 Analysis on supermanifolds or graded manifolds
58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
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