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Nichols algebras are an important tool for the classification of Hopfalgebras. Within those with finite GK dimension, we study homologicalinvariants of the super Jordan plane, that is, the Nichols algebra$A=B(V(-1,2))$. These invariants are Hochschild homology, the Hochschildcohomology algebra, the Lie structure of the first cohomology space - which isa 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 finitelygenerated, but not $K_2$ .

Homological invariants relating the super Jordan plane to the Virasoro algebra