Deforming $\mathcal{K}(1) $ superalgebra modules of symbols

Abstract

We study nontrivial deformations of the natural action of the Lie superalgebra $\mathcal{K}(1)$ of contact vector fields on the $(1,1)$-dimensional superspace $\mathbb{R}^{1|1}$ on the space of symbols $\widetilde{{\mathcal{S}}}_\delta^n=\bigoplus_{k=0}^n{\mathfrak{F}}_{\delta-\frac{k}{2}}$. We calculate obstructions for integrability of infinitesimal multiparameter deformations and determine the complete local commutative algebra corresponding to the miniversal deformation.