  Nichols algebras are an important tool for the classification of Hopf
algebras. Within those with finite GK dimension, we study homological
invariants of the super Jordan plane, that is, the Nichols algebra
$A=B(V(-1,2))$. These invariants are Hochschild homology, the Hochschild
cohomology algebra, the Lie structure of the first cohomology space - which is
a Lie subalgebra of the Virasoro algebra - and its representations $H^n(A,A)$
and also the Yoneda algebra. We prove that the algebra $A$ is $K_2$ . Moreover,
we prove that the Yoneda algebra of the bosonization of $A$ is also finitely
generated, but not $K_2$ .
