Third-order Jacobsthal generalized quaternions. (English) Zbl 1439.11038

Cerda-Morales, Gamaliel

J. Geom. Symmetry Phys. 50, 11-27 (2018).

Summary: 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.

MSC:

11B37	Recurrences
11R52	Quaternion and other division algebras: arithmetic, zeta functions
11Y55	Calculation of integer sequences

Keywords:

generalized quaternion; semi-quaternion; split quaternion; third-order Jacobsthal generalized quaternion; third-order Jacobsthal number