  We have recently shown that pseudo-bosonic operators realize concrete
examples of finite dimensional nilpotent Lie algebras over the complex field.
It has been the first time that such operators were analyzed in terms of
nilpotent Lie algebras (under prescribed conditions of physical character). On
the other hand, the general classification of a finite dimensional nilpotent
Lie algebra $\mathfrak{l}$ may be given via the size of its Schur multiplier
involving the so-called corank $t(\mathfrak{l})$ of $\mathfrak{l}$. We
represent $\mathfrak{l}$ by pseudo-bosonic ladder operators for
$t(\mathfrak{l}) \le 6$ and this allows us to represent $\mathfrak{l}$ when its
dimension is $\le 5$.
