A family of non-restricted D=11 geometric supersymmetries

We construct a two parameter family of eleven-dimensional indecomposable Cahen-Wallach spaces with irreducible, non-flat, non-restricted geometric supersymmetry of fraction $\nu=\tfrac{3}{4}$. Its compactified moduli space can be parametrized by a compact interval with two points corresponding to two non-isometric, decomposable spaces. These singular spaces are associated to a restricted $N=4$ geometric supersymmetry with $\nu=\tfrac{1}{2}$ in dimension six and a non-restricted $N=2$ geometric supersymmetry with $\nu=\tfrac{3}{4}$ in dimension nine.