Homology of Nilpotent Subalgebras of the Lie Superalgebra $K(1,1)$. 3

We calculate the dimensions of the second homology groups with trivial coefficients of nilpotent subalgebras of the Lie superalgebra $K(1,1)$, which is the natural superanalog of the Witt algebra. The proof is based on direct calculations of the rank of the differential. As an application, we find deformations of the maximal nilpotent subalgebra in $K(1,1)$.