论文标题
基本古典谎言超级级别的可及元素
Reachable elements in basic classical Lie superalgebras
论文作者
论文摘要
令\ Mathfrak {g} = \ Mathfrak {g} _ {\ bar {0}} \ oplus \ Mathfrak \ Mathfrak {g} _ {\ bar {1}}是基本的经典经典lie superalgebra，超过\ mathb {c}，e \ in \ mathak} nilpotent元素和\ mathfrak {g}^{e} e \ mathfrak {g}中的E e}。我们研究\ Mathfrak {g}中nilpotent元素的各种特性，这些元素以前仅在Lie代数中被考虑。特别是，我们证明当e满足\ mathfrak {g} = \ mathfrak {sl}（m | n），m \ neq n或\ mathfrak {psl {psl}（n | n）和\ mathfrak {osp {osp}（osp}（m | 2n）时，我们才证明e是可以达到的。对于特殊的Like superalgebras \ Mathfrak {g} = d（2,1;α），g（3），f（4），我们给出了E的分类，这些分类是可触及的，可触及的或满足Panyushev属性的。此外，我们为\ Mathfrak {g}^{e}及其中心\ Mathfrak {z}（\ Mathfrak {\ Mathfrak {g}^{e}）提供\ Mathfrak {g} = \ Mathfrak {g} \ Dim \ Mathfrak {Z}（\ Mathfrak {g}^{E}）和所有基本经典谎言superalgebras的标签dynkin图。
Let \mathfrak{g}=\mathfrak{g}_{\bar{0}}\oplus\mathfrak{g}_{\bar{1}} be a basic classical Lie superalgebra over \mathbb{C}, e\in\mathfrak{g}_{\bar{0}} a nilpotent element and \mathfrak{g}^{e} the centralizer of e in \mathfrak{g}. We study various properties of nilpotent elements in \mathfrak{g}, which have previously only been considered in the case of Lie algebras. In particular, we prove that e is reachable if and only if e satisfies the Panyushev property for \mathfrak{g}=\mathfrak{sl}(m|n), m\neq n or \mathfrak{psl}(n|n) and \mathfrak{osp}(m|2n). For exceptional Lie superalgebras \mathfrak{g}=D(2,1;α), G(3), F(4), we give the classification of e which are reachable, strongly reachable or satisfy the Panyushev property. In addition, we give bases for \mathfrak{g}^{e} and its centre \mathfrak{z}(\mathfrak{g}^{e}) for \mathfrak{g}=\mathfrak{psl}(n|n), which completes results of Han on the relationship between \dim\mathfrak{g}^{e}, \dim\mathfrak{z}(\mathfrak{g}^{e}) and the labelled Dynkin diagrams for all basic classical Lie superalgebras.
