论文标题
关于保存克利福德代数子空间的内形态度
On inner automorphisms preserving subspaces of Clifford algebras
论文作者
论文摘要
在本文中，我们考虑了内部自动形态，这些自动形态留下了不变的固定子空间，这是真实和复杂的Clifford代数 - 固定等级的子空间和由归还和等级相关的子空间的子空间。我们介绍了定义这种内部自动形态并研究其特性的元素组。这些谎言组中的一些可以解释为Clifford，Lipschitz和Spin群体的概括。我们研究相应的谎言代数。对于更一般的代数 - 分级的中央简单代数或分级的中央简单代数，可以重新对某些结果进行重新校正。
In this paper, we consider inner automorphisms that leave invariant fixed subspaces of real and complex Clifford algebras -- subspaces of fixed grades and subspaces determined by the reversion and the grade involution. We present groups of elements that define such inner automorphisms and study their properties. Some of these Lie groups can be interpreted as generalizations of Clifford, Lipschitz, and spin groups. We study the corresponding Lie algebras. Some of the results can be reformulated for the case of more general algebras -- graded central simple algebras or graded central simple algebras with involution.
