Fibonacci-Lucas Spinors Obtained from Hybrid Numbers

TL;DR

This paper introduces hybrid Fibonacci and Lucas spinor sequences derived from hybrid numbers, exploring their properties and polynomial extensions, with applications in mathematical physics, geometry, and number theory.

Contribution

It presents a novel concept of hybrid Fibonacci and Lucas spinors, defining their properties and polynomial sequences, expanding the mathematical framework of spinors and hybrid numbers.

Findings

Defined hybrid Fibonacci and Lucas spinor sequences.

Explored properties of these spinor sequences.

Introduced polynomial extensions of the spinor sequences.

Abstract

The aim of this work is to provide the contributors to journals or Hybrid numbers, akin to spinors, possess a broad range of applications in mathematical physics, geometry, and mathematics. In this study, these two significant topics were collectively addressed, introducing a new perspective to spinors and defining hybrid spinors, from which several basic properties were derived. Furthermore, by considering the Fibonacci and Lucas number sequences, subjects widely explored in number theory, the study defined hybrid Fibonacci and Lucas spinor sequences, examining some of their properties. Lastly, hybrid Fibonacci and Lucas polynomial spinor sequences have been introduced through the utilization of the polynomials associated with these number sequences.