The capability and certain functors of some nilpotent lie algebras of class two

Recently, the authors obtained the Schur multiplier, the non-abelian tensor square and the non-abelian exterior square of d-generator generalized Heisenberg Lie algebras of rank 1/2d(d - 1). Here, we intend to obtain the same results for d-generator generalized Heisenberg Lie algebras of rank t when 1/2d(d - 1) - 3 <= t <= 1/2d(d - 1) - 1. Then, as a result, we give similar consequences for a nilpotent Lie algebra L of class two when dim L-2 = t such that 1/2d(d - 1) -3 <= t <= 1/2d(d - 1) - 1.