# Identities for third order Jacobsthal quaternions

## TL;DR

This paper introduces third order Jacobsthal quaternions and Jacobsthal-Lucas quaternions, exploring their properties, relations to Jacobsthal numbers, and matrix representations.

## Contribution

It presents the first detailed study of third order Jacobsthal quaternions and their properties, expanding quaternion number theory.

## Key findings

- Derived properties of third order Jacobsthal quaternions
- Established relations with third order Jacobsthal numbers
- Provided matrix representations of these quaternions

## Abstract

In this paper we introduce the third order Jacobsthal quaternions and the third order Jacobsthal-Lucas quaternions and give some of their properties. We derive the relations between third order Jacobsthal numbers and third order Jacobsthal quaternions and we give the matrix representation of these quaternions.