We investigate the first cohomology space associated with the embedding of the Lie superalgebra K(2) of contact vector fields on the (1,2)-dimensional supercircle S 1|2 in the Lie superalgebra SΨDO(S 1|2 ) of superpseudodifferential operators with smooth coefficients. Following Ovsienko and Roger, we show that this space is ten-dimensional with only even cocycles and we give explicit expressions of the basis cocycles.

We study non-trivial deformations of the natural action of the Lie algebra Vect(R n ) on the space of differential forms on R n . We calculate abstractions for integrability of infinitesimal multi-parameter deformations and determine the commutative associative algebra corresponding to the miniversal deformation in the sense of [3].

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