On the super Jordan plane

We study algebraic properties of the super Jordan plane~$\mathcal B$ introduced by I. Angiono, I. Heckenberger and the first named author. Concretely we show that $\mathcal B$ is super-prime and has a super-simple super-artinian ring of fractions. We also compute the groups of superalgebra and braided Hopf algebra automorphisms. Instrumental for our approach is the embedding of the Jordan plane as a subalgebra of $\mathcal B$.