The second cohomology spaces of 풦(1) with coefficients in the superspace of weighted densities and deformations of the superspace of symbols on S1|1.

We explicitly describe the second cohomology of the Lie superalgebra 풦 ⁢ (1) of contact vector fields on the supercircle S 1 | 1 with coefficients in the spaces of weighted densities. We deduce the second cohomology of 풦 ⁢ (1) with coefficients in the Poisson algebra of pseudodifferential symbols on S 1 | 1 . We study formal deformations of the standard embedding of 풦 ⁢ (1) into the Poisson superalgebra of pseudodifferential symbols. [ABSTRACT FROM AUTHOR]