Deforming the Lie superalgebra of contact vector fields on $S^{1|2}$ inside the Lie superalgebra of pseudodifferential operators on $S^{1|2}$

We classify deformations of the standard embedding of the Lie superalgebra $\mathcal K(2)$ of contact vector fields on the $(1,2)$-dimensional supercircle into the Lie superalgebra $S\Psi D(S^{1|2})$ of pseudodifferential operators on the supercircle $S^{1|2}$. The proposed approach leads to the deformations of the central charge induced on $\mathcal K(2)$ by the canonical central extension of $S\Psi D(S^{1|2})$.