As in the Riemannian case there are semisimple symmetric spaces with "G" = "H" × "H". Any semisimple symmetric space is a product of symmetric spaces of this form with symmetric spaces such that formula_6 is simple. It remains to describe the latter case. For this, one needs to classify involutions "σ" of a (real) simple Lie algebra formula_6. If formula_38 is not simple, then formula_6 is a complex simple Lie algebra, and the corresponding symmetric spaces have the form "G"/"H", where "H" is a real form of "G": these are the analogues of the Riemannian symmetric spaces "G"/"K" with "G" a complex simple Lie group, and "K" a maximal compact subgroup.