Fibonacci Elliptic Biquaternions

Abstract

A. F. Horadam defined the complex Fibonacci numbers and Fibonacci quaternions in the middle of the 20th century. Half a century later, S. Hal{\i}c{\i} introduced the complex Fibonacci quaternions by inspiring from these definitions and discussed some properties of them. Recently, the elliptic biquaternions, which are generalized form of the complex and real quaternions, have been presented. In this study, we introduce the set of Fibonacci elliptic biquaternions that includes the set of complex Fibonacci quaternions as a special case and investigate some properties of Fibonacci elliptic biquaternions. Furthermore, we give the Binet formula and Cassini's identity in terms of Fibonacci elliptic biquaternions. Finally, we give elliptic and real matrix representations of Fibonacci elliptic biquaternions.