The diffeomorphism supergroup of a finite-dimensional supermanifold

TL;DR

This paper constructs the diffeomorphism supergroup of a compact finite-dimensional supermanifold as a Frechet supermanifold using categorical supergeometry, providing insights into its structure.

Contribution

It offers an explicit categorical construction of the diffeomorphism supergroup with a Frechet supermanifold structure, advancing supergeometry understanding.

Findings

Diffeomorphism supergroup has a Frechet supermanifold structure

Explicit categorical construction provided

Results on the structure of supergroups derived

Abstract

Using the categorical description of supergeometry we give an explicit construction of the diffeomorphism supergroup of a compact finite-dimensional supermanifold. The construction provides the diffeomorphism supergroup with the structure of a Frechet supermanifold. In addition, we derive results about the structure of diffeomorphism supergroups.