In this paper, the third-order Jacobsthal generalized quaternions are introduced. We use the well-known identities related to the third-order Jacobsthal and third-order Jacobsthal-Lucas numbers to obtain the relations regarding these quaternions. Furthermore, the third-order Jacobsthal generalized quaternions are classified by considering the special cases of quaternionic units. We derive the relations between third-order Jacobsthal and third-order Jacobsthal-Lucas generalized quaternions.
Gamaliel Cerda-Morales. "Third-Order Jacobsthal Generalized Quaternions." J. Geom. Symmetry Phys. 50 11 - 27, 2018. https://doi.org/10.7546/jgsp-50-2018-11-27