We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra. 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 algebra.
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