限制李代数的Toral稳定子
Toral stabilizers of restricted Lie algebras
摘要：
本文研究了定义在正特征的代数闭域$k$上的有限维限制李代数$(\mathfrak{g},[p])$的toral稳定子.计算了几类单李代数的环稳定子群，并给出了可解限制李代数的一个新刻画。此外，我们还确定了具有良好特征的例外单李代数的子代数结构。我们还提供了应用，其中涉及的权空间的分布。
英文摘要：
This paper investigates the toral stabilizer of a finite-dimensional restricted Lie algebra $(\mathfrak{g},[p])$, defined over an algebraically closed field $k$ of positive characteristic. We compute the group of toral stabilizers of some simple Lie algebras and give a new characterization of the solvable restricted Lie algebras. Moreover, we determine the subalgebra structure of exceptional simple Lie algebras in good characteristic. We also provide applications, which concern the distribution of weight spaces.
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