Affiliation:
1. KUTAHYA DUMLUPINAR UNIVERSITY
2. Kütahya Dumlupınar Üniversitesi
Abstract
In this paper, we established the connection between generalized quaternion algebra and real (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 Cl(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.
Publisher
Afyon Kocatepe Universitesi Fen Ve Muhendislik Bilimleri Dergisi
Reference16 articles.
1. Alagoz, Y. Oral, K.H. and Yuce, S., 2012. Split quaternion matrices. Miskolc Mathematical Notes, 13(2), 223–232.
2. Aragon, G., Aragon J.L. and Rodriguez, M.A., 1997. Clifford algebras and geometric Algebra. Adv. Appl. Clifford Al., 7(2), 91–102.
3. Ata, E. and Yaylı, Y., 2009. Split quaternions and semi-Euclidean projective spaces. Chaos, Solitons and Fractals, 41(4), 1910–1915.
4. Ata ,E., Kemer, Y. and Atasoy, A., 2012. Quadratic Formulas for Generalized Quaternions. Dumlupınar ¨Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 28, 27–34.
5. Ata, E. and Yıldırım, Y., 2018. A Different Polar Representation for Generalized and Generalized Dual Quaternions. Adv. Appl. Clifford Al., 28(4), 77.