论文标题
nilpotent元素的中央位置中心，超级级别
Centers of centralizers of nilpotent elements in exceptional Lie superalgebras
论文作者
论文摘要
令$ \ mathfrak {g} = \ mathfrak {g} _ {\ bar {0}} \ oplus \ mathfrak \ mathfrak \ Mathfrak {g} _ {\ bar {1}} $是有限的少量二型简单的superalgebera of类型$ \ mathbb {c} $。令$ g $为$ \ mathbb {c} $上的简单连接的半imple代数组，以便$ \ mathrm {lie}（g）= \ mathfrak {g} _ {\ bar {0}} $。假设$ e \ in \ mathfrak {g} _ {\ bar {0}} $是nilpotent。我们描述了$ \ mathfrak {g} $ in $ e $的centralizer $ \ mathfrak {g}^{e} $及其中心$ \ mathfrak {z}（\ sathfrak {\ mathfrak {g}^e}）$。我们还确定了$ e $的标记的dynkin图。我们证明定理将$ \ left（\ mathfrak {z}（\ mathfrak {g}^{e}）\ right）\ right）^{g^{e}} $和标记的dynkin图。
Let $\mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus\mathfrak{g}_{\bar{1}}$ be a finite-dimensional simple Lie superalgebra of type $D(2,1;α)$, $G(3)$ or $F(4)$ over $\mathbb{C}$. Let $G$ be the simply connected semisimple algebraic group over $\mathbb{C}$ such that $\mathrm{Lie}(G)=\mathfrak{g}_{\bar{0}}$. Suppose $e\in\mathfrak{g}_{\bar{0}}$ is nilpotent. We describe the centralizer $\mathfrak{g}^{e}$ of $e$ in $\mathfrak{g}$ and its centre $\mathfrak{z}(\mathfrak{g}^{e})$ especially. We also determine the labelled Dynkin diagram for $e$. We prove theorems relating the dimension of $\left(\mathfrak{z}(\mathfrak{g}^{e})\right)^{G^{e}}$ and the labelled Dynkin diagram.
