论文标题
在复杂的谎言代数的区域化中
On a quarternification of complex Lie algebras
论文作者
论文摘要
我们给出了季节谎言代数的定义和复杂的谎言代数的四方面化。根据我们的定义，gl（n，h），sl（n，h），so*（2n）和sp（n）分别是gl（n，c），sl（n，c），so（n，c）和u（n，c）和u（n）的四方面。然后，我们将证明一个简单的谎言代数承认了区域化。为了证明，由于Harich-Chandra，Chevalley和Serre，我们遵循众所周知的论点，从其相应的根系中构建了简单的谎言代数。将给出该区域谎言代数的根空间分解。基本根的每个根空间都是复杂的二维。
We give a definition of quarternion Lie algebra and of the quarternification of a complex Lie algebra. By our definition gl(n,H), sl(n,H), so*(2n) and sp(n) are quarternifications of gl(n,C), sl(n,C), so(n,C) and u(n) respectively. Then we shall prove that a simple Lie algebra admits the quarternification. For the proof we follow the well known argument due to Harich-Chandra, Chevalley and Serre to construct the simple Lie algebra from its corresponding root system. The root space decomposition of this quarternion Lie algebra will be given. Each root space of a fundamental root is complex 2-dimensional.
