A classical theorem of Veldkamp describes the center of an enveloping algebra of a Lie algebra of a semi-simple algebraic group in characteristic p. We generalize this result to a class of Lie algebras with a property that they arise as the reduction modulo $p\gg 0$ from an algebraic Lie algebra $\mathfrak{g}$, such that $\mathfrak{g}$ has no nontrivial semi-invariants in $\mathrm{Sym}(\mathfrak{g})$ and $\mathrm{Sym}{(\mathfrak{g})}^{\mathfrak{g}}$ is a polynomial algebra.

As an application, we solve the derived isomorphism problem of enveloping algebras for the above class of Lie algebras.

中文翻译：

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一类李代数的Veldkamp定理的推广

Veldkamp的一个经典定理描述了特征p中一个半简单代数群的Lie代数的一个包络代数的中心。我们将此结果推广到一类李式代数，其性质为归约模$p\gg 0$ 来自代数李代数 $\mathfrak{G}$，这样 $\mathfrak{G}$ 在中没有非平凡的半不变量 $\mathrm{象征}（\mathfrak{G}）$ 和 $\mathrm{象征}{（\mathfrak{G}）}^{\mathfrak{G}}$ 是多项式代数。

作为一种应用，我们解决了上述一类李代数的包络代数的导出同构问题。