COHOMOLOGY OF 𝔬𝔰𝔭(1|2) ACTING ON THE SPACE OF BILINEAR DIFFERENTIAL OPERATORS ON THE SUPERSPACE ℝ1|1

We compute the first cohomology of the ortosymplectic Lie superalgebra 𝔬𝔰𝔭(1|2) on the (1, 1)-dimensional real superspace with coefficients in the superspace 𝔇λ, μ of bilinear differential operators acting on weighted densities (λ ∈ ℝ2 and μ ∈ ℝ). This work is the simplest superization of a result by Bouarroudj [Cohomology of the vector fields Lie algebras on ℝℙ1 acting on bilinear differential operators, Int. J. Geom. Meth. Mod. Phys.2(1) (2005) 23–40].