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 ν=34. Its compactified moduli space can be parameterized 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 ν=12 in dimension six and a non-restricted N=2 geometric supersymmetry with ν=34 in dimension nine.