  We present here all the real algebras $\cal{A}$ with dim$\cal{A}\leq $5 and
all 6-dimensional nilpotent ones with symmetric, invariant and non-degenerate
metrics for which a WZW model can be constructed.
  In three and four dimensions there are no other algebras than the well known
$SU(2)$, $SU(1,1)$, $E_2^c$ and $H_4$. There exist only one five-dimensional
and one six-dimensional nilpotent algebra with invariant non-degenerate metric
and central charge $c=5, \,6$, respectively. We examine in details the
five-dimensional case and, by gauging an appropriate subgroup, four-dimensional
plane-wave string backgrounds are obtained. The corresponding background for
the six-dimensional case is flat.
