The affine cohomology spaces and its applications (Q2795364)

This paper gives the affine cohomology spaces associated with the affine algebra on the \((1,1)\)-dimensional real superspace. Let us recall that the \(n\)-th cohomology space of the orthosymplectic Lie superalgebra \(\mathrm{osp}(1,2)\) has been recently computed by \textit{D. Arnal} et al. [J. Math. Phys. 51, No. 9, 093517, 15 p. (2010; Zbl 1309.17001)]. In this work, the authors compute the \(n\)-th cohomology space of the affine Lie super algebra \(\mathrm{aff}(1)\). It is proved that this space is not trivial for \(n=0\) and \(n=1\). The results are applied to the module of weight densities and the module of linear differential operators acting on a superspace of weight densities. The purpose of this work is to study deformations on the \((1,1)\)-dimensional superspace.