Title: The structure, capability and the Schur multiplier of generalized Heisenberg Lie algebras,
Abstract: From [Problem 1729, Groups of prime power order, Vol. 3], Berkovich et al.
asked to obtain the Schur multiplier and the representation of a group $G$,
when $G$ is a special $p$-group minimally generated by $d$ elements and
$|G'|=p^{\frac{1}{2}d(d-1)}$. Since there are analogies between groups and Lie
algebras, we intend to give an answer to this question similarly for nilpotent
Lie algebras. Furthermore, we give some results about the tensor square and the
Schur multiplier of some nilpotent Lie algebras of class two.