Quaternion algebras and the generalized Fibonacci-Lucas quaternions

TL;DR

This paper introduces generalized Fibonacci-Lucas quaternions, proves they form an order in a quaternion algebra, and explores their properties, contributing to algebraic structure understanding.

Contribution

It is the first to define generalized Fibonacci-Lucas quaternions and establish their role as an order in quaternion algebra, expanding algebraic theory.

Findings

Generalized Fibonacci-Lucas quaternions form an order in a quaternion algebra

Properties of these quaternions are systematically investigated

The paper enhances understanding of algebraic structures involving Fibonacci-Lucas sequences

Abstract

In this paper, we introduce the generalized Fibonacci-Lucas quaternions and we prove that the set of these elements is an order,in the sense of ring theory, of a quaternion algebra. Moreover, we investigate some properties of these elements.