论文标题
关于2个可溶式Frobenius Lie代数的分类
On the classification of 2-solvable Frobenius Lie algebras
论文作者
论文摘要
我们讨论了2个可溶解的Frobenius Lie代数的分类。我们证明，每2个可溶解的frobenius躺在代数中，作为n维矢量空间V和V的全n维最大Abelian subergebra（MASA）的半方向总和，V。我们提供了v的全态空间。最大的Abelian nilpotent subgerbras（Mans），因此Kravchuk签名（n-1,0,1）。在低维度中，我们将所有2个可溶解的Frobenius分类为一般为Dimension 8。我们纠正并完成Winternitz和Zassenhaus的SL（4，R）Masas的分类列表。作为两种二元组，我们给出了一个简单的证据，证明了真实矢量空间的每个非构层室异常都可以接受约旦形式，并提供了SL（n，r）的cartan subgebras的新特征。
We discuss the classification of 2-solvable Frobenius Lie algebras. We prove that every 2-solvable Frobenius Lie algebra splits as a semidirect sum of an n-dimensional vector space V and an n-dimensional maximal Abelian subalgebra (MASA) of the full space of endomorphisms of V. We supply a complete classification of 2-solvable Frobenius Lie algebras corresponding to nonderogatory endomorphisms, as well as those given by maximal Abelian nilpotent subalgebras (MANS) of class 2, hence of Kravchuk signature (n-1,0,1). In low dimensions, we classify all 2-solvable Frobenius Lie algebras in general up to dimension 8. We correct and complete the classification list of MASAs of sl(4, R) by Winternitz and Zassenhaus. As a biproduct, we give a simple proof that every nonderogatory endormorphism of a real vector space admits a Jordan form and also provide a new characterization of Cartan subalgebras of sl(n, R).
