论文标题
谎言代数和固定前模块的半神经分解
Semisimple decompositions of Lie algebras and prehomogeneous modules
论文作者
论文摘要
我们研究{\ em diseimple} lie代数，即，可以将其写入两个半imple subergebras的矢量空间之和。我们表明，如果且仅当其可解决的自由基与其nilradical相吻合时，谎言代数$ \ mathfrak {g} $是不弥补的，并且是固定的$ \ mathfrak {s} $ - 用于Levi subalgebra $ \ Mathfrak的$ \ \ Mathfrak {s} $ $ Mathak的$ \ Mathfrak的模块。我们使用Vinberg给出的简单lie代数$ \ Mathfrak $ \ Mathfrak $ \ Mathfrak $ \ Mathfrak {S} $的分类，Vinberg给出了简单的Levi subelgebra的disemisimple lie代数的可解决的自由基。我们将此结果扩展到没有简单的$ a $的简单商。
We study {\em disemisimple} Lie algebras, i.e., Lie algebras which can be written as a vector space sum of two semisimple subalgebras. We show that a Lie algebra $\mathfrak{g}$ is disemisimple if and only if its solvable radical coincides with its nilradical and is a prehomogeneous $\mathfrak{s}$-module for a Levi subalgebra $\mathfrak{s}$ of $\mathfrak{g}$. We use the classification of prehomogeneous $\mathfrak{s}$-modules for simple Lie algebras $\mathfrak{s}$ given by Vinberg to show that the solvable radical of a disemisimple Lie algebra with simple Levi subalgebra is abelian. We extend this result to disemisimple Lie algebras having no simple quotients of type $A$.
