  We describe the infinitesimal deformations of the standard embedding of the
Lie superalgebra $D(2, 1 ; \alpha)$ into the Poisson superalgebra of
pseudodifferential symbols on $S^{1|2}$. We show that for the standard
embedding of $D(2, 1 ; \alpha)$ into the Poisson superalgebra of differential
operators on $S^{1|2}$, the infinitesimal deformations correspond to formal
deformations. For the embedding of $D(2, 1 ; \alpha)$ into the derived contact
superconformal algebra ${K}'(4)$, the infinitesimal deformations are formal
deformations.
