Homology and Cohomology of the Super Schrödinger Algebra $S\left(1/1\right)$ with Coefficients in the Trivial Module^*

In this paper we study the homology and cohomology groups of the super Schrödinger algebra $S\left(1/1\right)$ in (1 + 1)-dimensional spacetime. We explicitly compute the homology groups of $S\left(1/1\right)$ with coefficients in the trivial module. Then using duality, we finally obtain the dimensions of the cohomology groups of $S\left(1/1\right)$ with coefficients in the trivial module.