The Projective Linear Supergroup and the SUSY-preserving automorphisms of ${\mathbf P}^{1|1}$

SUSY $N$-supergroups and their real forms

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 $\mathbf{P}^{1|1}$.