论文标题
iwasawa撒谎超级甲壳虫的分解
Iwasawa Decomposition for Lie Superalgebras
论文作者
论文摘要
令$ \ mathfrak {g} $成为一个基本的简单谎言superalgebra，在代数封闭的特征零字段上，$θ$ $ \ mathfrak {g} $ conterrucion保留了不变的不变形式。我们证明$θ$或$δ\circθ$允许iWasawa分解，其中$δ$是规范分级自动形态$δ（x）=（ - 1）^{\ edimalline {x}}} x $。该证明使用了Serganova开发的广义根系的概念，并从更一般的结果遵循了来自Lie Superalgebra $ \ Mathfrak {G} $的某些托里的中心化。
Let $\mathfrak{g}$ be a basic simple Lie superalgebra over an algebraically closed field of characteristic zero, and $θ$ an involution of $\mathfrak{g}$ preserving a nondegenerate invariant form. We prove that either $θ$ or $δ\circθ$ admits an Iwasawa decomposition, where $δ$ is the canonical grading automorphism $δ(x)=(-1)^{\overline{x}}x$. The proof uses the notion of generalized root systems as developed by Serganova, and follows from a more general result on centralizers of certain tori coming from semisimple automorphisms of the Lie superalgebra $\mathfrak{g}$.
