Abstract
We study the homology and cohomology groups of super Lie algebras of supersymmetries and of super Poincaré Lie algebras in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions ⩽11. For dimensions D = 10 , 11 we describe also the cohomology of reduction of supersymmetry Lie algebra to lower dimensions. Our methods can be applied to extended supersymmetry Lie algebras.
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