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Homology and cohomology of the super Schrödinger algebra

Abstract In this article, we study the homology and cohomology groups of the super Schrödinger algebra in (1 + 1)-dimensional spacetime. We explicitly compute the homology groups of with coefficients in finite-dimensional irreducible representations. Then using the duality between homology and cohomology, we finally obtain the dimensions of the cohomology groups of with coefficients in finite-dimensional irreducible representations.