Homology of Lie algebra of supersymmetries and of super Poincaré Lie algebra

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=10,11D=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.