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On Inner Automorphisms Preserving Fixed Subspaces of Clifford Algebras
Advances in Applied Clifford Algebras ( IF 1.5 ) Pub Date : 2021-04-09 , DOI: 10.1007/s00006-021-01135-6
Dmitry Shirokov

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.



中文翻译:

关于Clifford代数固定子空间的内自同构。

在本文中,我们考虑内部自同构,它保留了实数和复数Clifford代数的不变固定子空间-固定等级的子空间和由回归和等级对合确定的子空间。我们介绍定义此类内部自同构的元素组并研究其属性。这些李群中的一些可以解释为Clifford,Lipschitz和spin群的概括。我们研究相应的李代数。对于更通用的代数(渐变中央简单代数或带对合的渐变中央简单代数),某些结果可以重新表述。

更新日期:2021-04-09
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