Flat pseudo-Riemannian homogeneous spaces with non-abelian holonomy group (Q2845063)

In an earlier paper [\textit{O. Baues}, IRMA Lect. Math. Theor. Phys. 16, 731--817 (2010; Zbl 1205.53022)] it was shown that a compact complete flat homogeneous pseudo-Riemannian manifold may have a non-abelian fundamental group. In the paper under review some related new results are presented. Among other things, it is demonstrated that the linear holonomy group of a compact flat homogeneous pseudo-Riemannian manifold is always abelian. Also, it is shown that every homogeneous flat pseudo-Riemannian manifold of dimension less than eight has abelian linear holonomy, while in eight dimensions a counter-example is constructed. This counter-example is a non-complete pseudo-Riemannian manifold of signature \((4,4)\). A complete flat homogeneous pseudo-Riemannian manifold with non-abelian linear holonomy is constructed with signature \((7,7)\), i.e., in fourteen dimensions.