Cohomology of κ(2) Acting on Linear Differential Operators on the Superspace ℝ

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We compute the first differential cohomology of the Lie superalgebra κ(2) of contact vector fields on the (1, 2)-dimensional real superspace with coefficients in the superspace of linear differential operators between the superspaces of weighted densities—a superisation of a result by Feigin and Fuchs. We give explicit expressions of 1-cocycles generating these spaces.

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