A Note on Centralizers and Twisted Centralizers in Clifford Algebras

TL;DR

This paper characterizes centralizers and twisted centralizers in Clifford algebras, providing explicit forms for various subspaces, which can aid applications in computer science, physics, and engineering.

Contribution

It offers explicit formulas for centralizers and twisted centralizers in Clifford algebras, extending understanding of their structure for different subspaces.

Findings

Explicit forms of centralizers for fixed grade subspaces

Explicit forms of twisted centralizers for subspaces defined by involutions

Potential applications in physics, computer science, and engineering

Abstract

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.