Authors:Nizar Ben Fraj, Hafedh Khalfoun and Imed Basdouri
We compute the second differential osp(n|2)-relative cohomology of the Lie superalgebra К(n) of contact vector fields with coefficients in the superspace of weighted densities on the (1, n)-dimensional real superspace, n > 1, where osp(n|2) is the orthosymplectic Lie superalgebra. We explicitly give 2-cocycles spanning theses cohomology spaces. This work is the simplest generalization of a result by Basdouri [ On osp(1|2)-Relative Cohomology on S1|1. Communications in Algebra 42:4, 1698–1710 (2014)].
Authors:Nader Belghith, Mabrouk Ben Ammar and Nizar Ben Fraj
Over the (1, 1)-dimensional real supercircle, we consider the K(1)-modules Dλ,μk of linear differential operators of order k acting on the superspaces of weighted densities, where K(1) is the Lie superalgebra of contact vector fields. We give, in contrast to the classical setting, a classification of these modules. This work is the simplest superization of a result by Gargoubi and Ovsienko.