  The classification of the holonomy algebras of Lorentzian manifolds can be
reduced to the classification of irreducible subalgebras
$\mathfrak{h}\subset\mathfrak{so}(n)$ that are spanned by the images of linear
maps from $\mathbb{R}^n$ to $\mathfrak{h}$ satisfying an identity similar to
the Bianchi one. T. Leistner found all such subalgebras and it turned out that
the obtained list coincides with the list of irreducible holonomy algebras of
Riemannian manifolds. The natural problem is to give a simple direct proof to
this fact. We give such proof for the case of semisimple not simple Lie
algebras $\mathfrak{h}$.
