This paper investigates centralizers and twisted centralizers in degenerate and non-degenerate Clifford (geometric) algebras. We provide an explicit form of the centralizers and twisted centralizers of the subspaces of fixed grades, subspaces determined by the grade involution and the reversion, and their direct sums. The results can be useful for applications of Clifford algebras in computer science, physics, and engineering.

中文翻译：

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关于克利福德代数中的扶正器和扭曲扶正器的注解

本文研究了简并和非简并 Clifford（几何）代数中的中心化器和扭曲中心化器。我们提供了固定等级子空间、由等级对合和回归确定的子空间以及它们的直和的集中器和扭曲集中器的显式形式。结果对于克利福德代数在计算机科学、物理学和工程中的应用很有用。