Fibonacci Elliptic Biquaternions

Abstract

A. F. Horadam defined the complex Fibonacci numbers and Fibonacci quaternions in themiddle of the 20th century. Half a century later, S. Halıcı introduced the complex Fibonacciquaternions by inspiring from these definitions and discussed some properties of them.Recently, the elliptic biquaternions, which are generalized form of the complex and realquaternions, have been presented. In this study, we introduce the set of Fibonacci ellipticbiquaternions that includes the set of complex Fibonacci quaternions as a special case, andinvestigate some properties of Fibonacci elliptic biquaternions. Furthermore, we give theBinet formula and Cassini’s identity in terms of Fibonacci elliptic biquaternions. Finally,we give elliptic and real matrix representations of Fibonacci elliptic biquaternions.