On some Properties of Generalized Tribonacci Spinors

TL;DR

This paper introduces Tribonacci spinors based on generalized Tribonacci quaternions, explores their algebraic structure, and derives key formulas like Binet and Cassini analogs for these mathematical objects.

Contribution

It presents the first mathematical definition and algebraic framework for Tribonacci spinors, extending quaternion-based spinor concepts with new formulas.

Findings

Established algebraic structure of Tribonacci spinors

Derived Binet-like formulas for Tribonacci spinors

Proved Cassini-like identities for these spinors

Abstract

Spinors are used in physics quite extensively. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined Tribonacci spinors using the generalized Tribonacci quaternions. Later, we have established the structure of algebra for these spinors. Finally, we have proved some important formulas such as Binet and Cassini-like formulas which are given for some series of numbers in mathematics for Tribonacci spinors.