Third-order Jacobsthal Generalized Quaternions
Gamaliel Cerda-Morales
TL;DR
This paper introduces third-order Jacobsthal generalized quaternions, explores their properties using known identities, and classifies them based on quaternionic units, establishing relations with Jacobsthal-Lucas quaternions.
Contribution
It presents the first comprehensive study of third-order Jacobsthal generalized quaternions, including their classification and interrelations with Jacobsthal-Lucas quaternions.
Findings
Derived identities for third-order Jacobsthal quaternions
Classified quaternions based on quaternionic units
Established relations with Jacobsthal-Lucas quaternions
Abstract
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.
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