Let L be a finite-dimensional nilpotent Lie algebra of class two over a field $\mathbb{F}$ of characteristic different from two. The aim of the present paper is to give an upper bound for the dimension of the center factor L/Z(L) of a capable Lie algebra L. As a result, we also find a lower bound for the dimension of the derived subalgebra L² for a capable Lie algebra L. Furthermore, we also give some criteria for determining the capability of L.

中文翻译：

---

二类能幂零李代数中心因子维数的界

令L为域上的二类有限维幂零李代数$\mathbb{F}$两个不同的特性。本论文的目的是给出一个有能力的李代数L的中心因子L / Z ( L )的维数上限。结果，我们还找到了一个有能力的李代数L的派生子代数L ²维数的下界。此外，我们还给出了一些用于确定L能力的标准。