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On the Cohomology of the Lie Superalgebra of Contact Vector Fields on $S^{1|2}$
Boujemaa Agrebaoui1, Nizar Ben Fraj1, Salem Omri1

We investigate the first cohomology space associated with the embedding of the Lie superalgebra $\cK(2)$ of contact vector fields on the (1,2)-dimensional supercircle $S^{1\mid 2}$ in the Lie superalgebra $\cS\Psi \cD \cO(S^{1\mid 2})$ 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.
1 :  Laboratoire d'Analyse Harmonique de Sfax