论文标题
亚伯利亚理想和拉格朗日亚级别的多种多样
Abelian Ideals and the Variety of Lagrangian Subalgebras
论文作者
论文摘要
对于一个半个代数$ g $的伴随类型的$ g $，带有lie代数$ \ mathfrak g $在复数上，我们在集团$ g \ ltimes \ ltimes \ mathfrak g^{\ ast} $ lagrangian subgebras of $ salgebras a $ \ matherfrak f \ ltfrime the groun of $ g \ ltimes \ ltimes \ ltimes \ ltimes \ mathfrak g^{ g^{\ ast} $和$ \ mathfrak g $的固定Borel subgerbra的Abelian理想集。特别是，此类轨道的数量等于$ 2^{\ text {rk} \ Mathfrak g} $，由彼得森（Peterson）的Abelian理想定理。
For a semisimple algebraic group $G$ of adjoint type with Lie algebra $\mathfrak g$ over the complex numbers, we establish a bijection between the set of closed orbits of the group $G \ltimes \mathfrak g^{\ast}$ acting on the variety of Lagrangian subalgebras of $\mathfrak g \ltimes \mathfrak g^{\ast}$ and the set of abelian ideals of a fixed Borel subalgebra of $\mathfrak g$. In particular, the number of such orbits equals $2^{\text{rk} \mathfrak g}$ by Peterson's theorem on abelian ideals.
