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 $\frac{1}{2}d(d-1)-3\le t\le \frac{1}{2}d(d-1)-1.$ 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 $\frac{1}{2}d(d-1)-3\le t\le \frac{1}{2}d(d-1)-1.$

中文翻译：

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二类幂零谎言代数的能力和某些函子

最近，作者得到了秩的d-生成器广义海森堡李代数的Schur乘数、非阿贝尔张量平方和非阿贝尔外平方$\frac{\mathrm{1个}}{\mathrm{2个}}d(d-\mathrm{1个}).$在这里，我们打算对秩为t的d生成元广义海森堡李代数获得相同的结果，当$\frac{\mathrm{1个}}{\mathrm{2个}}d(d-\mathrm{1个})-\mathrm{3个}\le 吨\le \frac{\mathrm{1个}}{\mathrm{2个}}d(d-\mathrm{1个})-1.$然后，作为结果，我们对第二类的幂零李代数L给出类似的结果，当$\mathrm{暗淡}(\mathrm{大号}/Z(\mathrm{大号}))=d,$ $\mathrm{暗淡}{\mathrm{大号}}^{\mathrm{2个}}=吨$这样$\frac{\mathrm{1个}}{\mathrm{2个}}d(d-\mathrm{1个})-\mathrm{3个}\le 吨\le \frac{\mathrm{1个}}{\mathrm{2个}}d(d-\mathrm{1个})-1.$