SUSY $N$-supergroups and their real forms

TL;DR

This paper classifies and explicitly constructs SUSY N-supergroups for N=1,2, explores their real forms, and identifies the supergroup of SUSY automorphisms of complex supermanifolds.

Contribution

It provides a detailed classification and explicit realization of SUSY N-supergroups and their real forms, including automorphism supergroups of supermanifolds.

Findings

Classification of SUSY N-supergroups for N=1,2

Explicit realization of these supergroups

Identification of SUSY automorphism supergroups of supermanifolds

Abstract

We study SUSY $N$-supergroups, $N=1,2$, their classification and explicit realization, together with their real forms. In the end, we give the supergroup of SUSY preserving automorphism of $\mathbf{C}^{1|1}$ and we identify it with a subsupergroup of the SUSY preserving automorphisms of $\mathbf{P}^{1|1}$.