(1) Département de Mathématiques, Faculté des Sciences de Sfax, BP 802, 3038 Sfax, Tunisie
Abstract:
We compute the first cohomology spaces of the Lie superalgebra with coefficients in the superspace of linear differential operators acting on weighted densities on the supercircle S1|1. The structure of these spaces was conjectured in (Gargoubi et al. in Lett Math Phys 79:5165, 2007). In fact, we prove here that the situation is a little bit more complicated.