论文标题
二次谎言代数的示例和模式
Examples and patterns on quadratic Lie algebras
论文作者
论文摘要
如果谎言代数符合对称不变且非脱线的双线性形式，则据说是二次的。具有杀戮形式的半圣代数是这些代数的示例，而正交子空间则提供ABELIAN二次代数。二次代数的类别很耗尽，但乍一看，代数是二次的天气。由于存在不变的形式力元素模式，因此出现了一些必要的结构条件。沿本文，我们概述了有关该主题的经典特征和构造，并关注局部二次的存在和构造。
A Lie algebra is said to be quadratic if it admits a symmetric invariant and non-degenerated bilinear form. Semisimple algebras with the Killing form are examples of these algebras, while orthogonal subspaces provide abelian quadatric algebras. The class of quadratic algebras is outsize, but at first sight it is not clear weather an algebra is quadratic. Some necessary structural conditions appear due to the existence of an invariant form forces elemental patterns. Along the paper we overview classical features and constructions on this topic and focus on the existence and constructions of local quadratic.
