Generalized Quaternions and Matrix Algebra

Authors : Erhan ATA, Ümit Ziya SAVCI

Pages : 638-647

Doi:10.35414/akufemubid.1182145

View : 36 | Download : 30

Publication Date : 2023-06-28

Article Type : Research Paper

Abstract :In this paper, we established the connection between generalized quaternion algebra and real insert ignore into journalissuearticles values(complex); matrix algebras by using Hamilton operators. We obtained real and complex matrices corresponding to the real and complex basis of the generalized quaternions. Also, we investigated the basis features of real and complex matrices. We get Pauli matrices corresponding to generalized quaternions. Then, we have shown that the algebra produced by these matrices is isomorphic to the Clifford algebra Clinsert ignore into journalissuearticles values(E_αβ^3); produced by generalized space E_αβ^3. Finally, we studied the relations among the symplectic matrices group corresponding to generalized unit quaternions, generalized unitary matrices group, and generalized orthogonal matrices group.
Keywords : Genelleştirilmiş kuaterniyonlar, Hamilton operatörleri, Pauli matrisleri, Genelleştirilmiş üniter matrisler, Genelleştirilmiş ortogonal matrisler