On the second cohomology of the affine superalgebra

R. Messaoud, M. Boujelben, A. Braghtha, M. E. Chraygui

We compute the second cohomology of the affine Lie superalgebra aff(1|1) on the (1,1)-dimensional real superspace with coefficients in the superspace Dλ,ν;μ of bilinear differential operators acting on weighted densities and with coefficients in the superspace Dλ1,λ2,λ3;μ of trilinear differential operators acting on weighted densities. We explicitly give 2-cocycles spanning these cohomology. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(3) (2025), pp. 61-77