论文标题
谎言p-algebras的模量
Moduli of Lie p-algebras
论文作者
论文摘要
在本文中，我们研究了有限维谎言代数的模量空间与平坦中心，证明了Lie P-Elgebras的健忘地图以谎言代数是一种仿射纤维，我们指出了存在P映射的新案例。然后，我们为等级3的特殊情况说明了这些结果，等级3的特殊情况是我们在Z上构建和研究的模量空间。我们在有限级别的当地自由级别的局部自由级别的p-代数之间扩展了类别的经典等效性，其高度为1的本地自由组方案，表明这些对象的中心彼此相对应。我们通过分析等级3的P-lie代数的模量的平滑度，特别是识别一些平滑的组件。
In this paper, we study moduli spaces of finite-dimensional Lie algebras with flat center, proving that the forgetful map from Lie p-algebras to Lie algebras is an affine fibration, and we point out a new case of existence of a p-mapping. Then we illustrate these results for the special case of Lie algebras of rank 3, whose moduli space we build and study over Z. We extend the classical equivalence of categories between locally free Lie p-algebras of finite rank with finite locally free group schemes of height 1, showing that the centers of these objects correspond to each other. We finish by analysing the smoothness of the moduli of p-Lie algebras of rank 3, in particular identifying some smooth components.
