AI 中文总结
该研究证明任意n维光滑仿射代数簇上向量场李代数的括号宽度有上界，还对特定簇给出改进界，丰富了李代数相关代数几何问题的结论。
AI 中文摘要
我们证明，任意n维光滑仿射代数簇上的向量场李代数的括号宽度至多为(n+1)²；对部分ℂ*簇家族给出了改进的界，特别是对SLₙ(ℂ)和Koras–Russell三次三维体。
英文摘要
We prove that the bracket width of the Lie algebra of vector fields on any smooth affine algebraic variety of dimension $n$ is at most $(n+1)^2$. We give improved bounds for some families of $\mathbb{C}^*$-varieties, in particular for $\mathrm{SL}_n(\mathbb{C})$ and for the Koras--Russell cubic threefold.
Comments11 pages
