Finslerian N-spinor algebra

TL;DR

This paper introduces Finslerian N-spinors, develops their algebra, and explores their connection to higher-dimensional Finslerian spaces, generalizing classical spinor-group relationships.

Contribution

It presents the mathematical formulation of Finslerian N-spinors and extends the SL(2,C) to SL(N,C) epimorphism to higher dimensions.

Findings

Finslerian N-spinors are linked to N^2-dimensional flat Finslerian space

Developed the algebraic structure of Finslerian N-spinors

Generalized the SL(2,C) to SL(N,C) group epimorphism

Abstract

New mathematical objects called Finslerian N-spinors are discussed. The Finslerian N-spinor algebra is developed. It is found that Finslerian N-spinors are associated with an N^2-dimensional flat Finslerian space. A generalization of the epimorphism SL(2,C) --> SO^\uparrow(1,3) to a case of the group SL(N,C) is constructed.