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

Abstract

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 $ \\frac{1}{2}d(d-1).$ Here, we intend to obtain the same results for $d$-generator generalized Heisenberg Lie algebras of rank $ t$ when $ \\frac{1}{2}d(d-1)-3 \\leq t\\leq \\frac{1}{2}d(d-1)-1.$ Then, as a result, we give similar consequences for a nilpotent Lie algebra $ L $ of class two when $ \\dim (L/Z(L))=d,$ $ \\dim L^2=t $ such that $ \\frac{1}{2}d(d-1)-3 \\leq t\\leq \\frac{1}{2}d(d-1)-1.$