Homology and Cohomology of the Super Schrödinger Algebra S(1/1) with Coefficients in the Trivial Module

Abstract

In this paper we study the homology and cohomology groups of the super Schrödinger algebra [Formula: see text] in (1 + 1)-dimensional spacetime. We explicitly compute the homology groups of [Formula: see text] with coefficients in the trivial module. Then using duality, we finally obtain the dimensions of the cohomology groups of [Formula: see text] with coefficients in the trivial module.