A Note on Centralizers and Twisted Centralizers in Clifford Algebras

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.

arXiv comment22 pages

References in corpus (8)

• Geometric Algebras for Euclidean Geometry
• Clifford algebras and their applications to Lie groups and spinors
• Quaternion typification of Clifford algebra elements
• Graded Symmetry Groups: Plane and Simple
• Development of the method of quaternion typification of Clifford algebra elements
• On inner automorphisms preserving subspaces of Clifford algebras
• On generalization of Lipschitz groups and spin groups
• On Some Lie Groups in Degenerate Clifford Geometric Algebras

Cited by in corpus (2)

• Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras
• On Lie Groups Preserving Subspaces of Degenerate Clifford Algebras