On some Properties of Generalized Tribonacci Spinors
Gamaliel Cerda-Morales
TL;DR
The paper develops a spinor formulation for generalized Tribonacci quaternions by defining quaternions $Q_{v,n}$ from generalized Tribonacci numbers $V_n$ and mapping them to spinors via $A_{v,n}=\left[V_{n+3}+iV_nV_{n+1}+iV_{n+2}\right]$. It establishes a linear, injective correspondence between the Tribonacci quaternion family $\mathbb{T}_{r,s,t}$ and spinors, and derives Binet-type expressions, generating functions, conjugates, norms, and determinant relations within this spinor framework. The work further extends these results to Tribonacci spinors and associated matrices, providing a cohesive algebraic and analytic toolkit for recurrence-based spinor-quaternion structures. Overall, the study links spinor-quaternion algebra with Tribonacci-type sequences, enabling new geometric interpretations and potential applications in algebra, geometry, and physics.
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.