泛欧氏空间的Clifford群、扭群、旋群及它们的李代数

摘要

本文研究了泛欧氏空间的Clifford群、扭群、旋群,它们为Clifford代数中选出极好的一类子群.利用Clifford代数理论方法,获得了泛欧氏空间中Clifford群、扭群、旋群及其李代数的结构及它们之间的关系,并且得到了它们的李代数.%In this article, we discuss the Clifford groups, the pin groups and the spin groups in universal Euclidean spaces. These groups are certain well chosen subgroups of Clifford algebras.By using Clifford algebra theory, we get the structure of these groups and the relationships amongthem, and also the Lie algebras of these groups.