$4 \times 4 $ Matrix Representations of Hurwitz Split Quaternions
Abstract
In this paper, we investigate the algebraic properties of Hurwitz split quaternions through their matrix representations. We construct the $4 \times 4$ left and right matrix representations and demonstrate that they have a specific block structure. Furthermore, we establish that the left representation is a homomorphism, while the right representation is an anti-homomorphism. Finally, we investigate certain properties of these matrices, proving that the trace is always an even integer and the determinant corresponds to the square of the split quaternion norm.
Keywords
References
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Details
Primary Language
English
Subjects
Algebra and Number Theory
Journal Section
Research Article
Authors
Publication Date
March 30, 2026
Submission Date
November 29, 2025
Acceptance Date
March 2, 2026
Published in Issue
Year 2026 Number: 54