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Summary:
The author studies the holonomy group of a simply connected indecomposable and reducible Lorentzian spin manifold under the condition that they admit parallel spinors. He shows that there are only two possible situations: either the manifold is a so-called Brinkmann wave or it has Abelian holonomy and is a pp-manifold -- a generalization of a plane-wave. The author gives also sufficient conditions for a Brinkmann wave to have as holonomy the semidirect product of holonomy group of a Riemannian manifold and $\bbfR^n$, and gives examples starting with K\"ahler and hyper-K\"ahler manifolds.
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