Torsion-free G_{2(2)}^*-structures with full holonomy on nilmanifolds

We study the existence of invariant metrics with holonomy G∗2(2)⊂SO(4,3) on compact nilmanifolds, i.e. on compact quotients of nilpotent Lie groups by discrete subgroups. We prove that, up to isomorphism, there exists only one indecomposable nilpotent Lie algebra admitting a torsion-free G∗2(2)-structure such that the center is definite with respect to the induced inner product. In particular, we show that the associated compact nilmanifold admits a 3-parameter family of invariant metrics with full holonomy G∗2(2).