论文标题
关于borel lie subergebra的Drinfel'd的自动形态学
On the automorphisms of the Drinfel'd double of a Borel Lie subalgebra
论文作者
论文摘要
令$ {\ mathfrak g} $为Borel subalgebra $ {\ Mathfrak b} $的复杂简单的Lie代数。考虑半程产品$ i {\ mathfrak b} = {\ Mathfrak b} \ ltimes {\ Mathfrak b}^*$，其中dual $ {\ mathfrak b}^*$ of $ {\ mathfrak b} $的配置，是$ { $ i {\ mathfrak b} $。我们描述了lie algebra $ i {\ mathfrak b} $的自动形态组$ {\ operatorName {aut}}（i {\ mathfrak b}）$。特别是我们证明它包含$ {\ mathfrak b} $的扩展Dynkin图的自动构态组。在类型$ a_n $中，最近证明，二面亚组包含在$ {\ operatorname {aut}}（i {\ mathfrak b}）$ in arxiv中的roland van der veen in arxiv：roland van der veen in arxiv：2002.002.00697（wher u} _n $）。他们的构造是手工制作的，他们要求提供解释：此注释充分回答了这个问题。
Let ${\mathfrak g}$ be a complex simple Lie algebra with Borel subalgebra ${\mathfrak b}$. Consider the semidirect product $I{\mathfrak b}={\mathfrak b}\ltimes{\mathfrak b}^*$, where the dual ${\mathfrak b}^*$ of ${\mathfrak b}$, is equipped with the coadjoint action of ${\mathfrak b}$ and is considered as an abelian ideal of $I{\mathfrak b}$. We describe the automorphism group ${\operatorname{Aut}}(I{\mathfrak b})$ of the Lie algebra $I{\mathfrak b}$. In particular we prove that it contains the automorphism group of the extended Dynkin diagram of ${\mathfrak b}$. In type $A_n$, the dihedral subgroup was recently proved to be contained in ${\operatorname{Aut}}(I{\mathfrak b})$ by Dror Bar-Natan and Roland Van Der Veen in arXiv:2002.00697 (where $I{\mathfrak b}$ is denoted by $I{\mathfrak u}_n$). Their construction is handmade and they ask for an explanation: this note fully answers the question.
