  Together with spaces of constant sectional curvature and products of a real
line with a manifold of constant curvature, the socalled Egorov spaces and
$\varepsilon$-spaces exhaust the class of $n$-dimensional Lorentzian manifolds
admitting a group of isometries of dimension at least ${1/2} n(n-1)+1$, for
almost all values of $n$ [Patrangenaru V., Geom. Dedicata 102 (2003), 25-33].
We shall prove that the curvature tensor of these spaces satisfy several
interesting algebraic properties. In particular, we will show that Egorov
spaces are Ivanov-Petrova manifolds, curvature-Ricci commuting (indeed,
semi-symmetric) and $\mathcal P$-spaces, and that $\varepsilon$-spaces are
Ivanov-Petrova and curvature-curvature commuting manifolds.
