jnt Journal of New Theory 2149-1402 Naim ÇAĞMAN 10.53570/jnt.1832707 Algebra and Number Theory Cebir ve Sayı Teorisi $4 \times 4 $ Matrix Representations of Hurwitz Split Quaternions https://orcid.org/0000-0002-7403-8701 Özbay Neslihan Ayşen ÇANKAYA ÜNİVERSİTESİ 03 30 2026 54 1 11 11 29 2025 03 02 2026 Copyright © 2014, Journal of New Theory 2014 Journal of New Theory

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.

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