We study the homology and cohomology groups of super Lie algebra of
supersymmetries and of super Poincare Lie algebra 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 algebra.Comment: New version with some additions and correction
