论文标题
关于Lipschitz组和自旋组的概括
On generalization of Lipschitz groups and spin groups
论文作者
论文摘要
本文介绍了一些新的谎言组，这些基团保存了扭曲的伴随表示下的几何代数（或克利福德代数）的固定子空间。我们考虑由固定等级和子空间的子空间的案例，由等级相关性和回归确定。一些被考虑的谎言组可以解释为Lipschitz组和旋转组的概括。 Lipschitz组和自旋组是这些谎言组的亚组，并在小尺寸的情况下与它们重合。我们研究相应的谎言代数。
This paper presents some new Lie groups preserving fixed subspaces of geometric algebras (or Clifford algebras) under the twisted adjoint representation. We consider the cases of subspaces of fixed grades and subspaces determined by the grade involution and the reversion. Some of the considered Lie groups can be interpreted as generalizations of Lipschitz groups and spin groups. The Lipschitz groups and the spin groups are subgroups of these Lie groups and coincide with them in the cases of small dimensions. We study the corresponding Lie algebras.
