Extracta Mathematicae (Dec 2019)
aff(1|1)-trivial deformations of aff(2|1)-modules of weighted densities on the superspace
Abstract
Over the (1|2)-dimensional real superspace, we study aff(1|1)-trivial deformations of the action of the affine Lie superalgebra aff(2|1) on the direct sum of the superspaces of weighted densities. We compute the necessary and sufficient integrability conditions of a given infinitesimal deformation of this action and we prove that any formal deformation is equivalent to its infinitisemal part.