论文标题
基本古典谎言中的nilpotent元素的中心化良好特征
Centralizers of nilpotent elements in basic classical Lie superalgebras in good characteristic
论文作者
论文摘要
令\ Mathfrak {g} = \ Mathfrak {g} _ {\ bar {0}} \ oplus \ mathfrak \ Mathfrak {g} _ {\ bar {1}}是一个基本的经典谎言，是一个基本的superalgebra，在代数封闭的字段上是一个超级封闭的字段\ mathbb {mathbb {令g _ {\ bar {0}}为\ mathbb {k}的还原代数组，以便\ mathrm {lie}（g _ {\ bar {0}}} = \ mathfrak {g _ {\ bar {0}）= \ mathfrak {g}假设e \ in \ mathfrak {g} _ {\ bar {0}}是nilpotent。为\ Mathfrak {g}和\ Mathfrak {Z}（\ Mathfrak {g}^{e}）的e in \ mathfrak {g}和\ mathfrak in in \ mathfrak {g}中的中心{g}^{e}编写\ mathfrak {我们通过使用关联的Cocharactersτ：\ Mathbb {k}^{k}^{\ times} \ rightArrow g _ {0} 0}}的基础来计算\ mathfrak {g}^{e}和\ mathfrak {z}（\ mathfrak {g}^{e}）。此外，我们给出了E的分类，这些分类是可以达到的，可触及的或满足特殊的lie superalgebras d（2,1;α），g（3）和f（4）的panyushev特性。
Let \mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus\mathfrak{g}_{\bar{1}} be a basic classical Lie superalgebra over an algebraically closed field \mathbb{K} whose characteristic p>0 is a good prime for \mathfrak{g}. Let G_{\bar{0}} be the reductive algebraic group over \mathbb{K} such that \mathrm{Lie}(G_{\bar{0}})=\mathfrak{g}_{\bar{0}}. Suppose e\in\mathfrak{g}_{\bar{0}} is nilpotent. Write \mathfrak{g}^{e} for the centralizer of e in \mathfrak{g} and \mathfrak{z}(\mathfrak{g}^{e}) for the centre of \mathfrak{g}^{e}. We calculate a basis for \mathfrak{g}^{e} and \mathfrak{z}(\mathfrak{g}^{e}) by using associated cocharacters τ:\mathbb{K}^{\times}\rightarrow G_{\bar{0}} of e. In addition, we give the classification of e which are reachable, strongly reachable or satisfy the Panyushev property for exceptional Lie superalgebras D(2,1;α), G(3) and F(4).
