Nonlinear Relativistic Invariance For Quadrahyperbolic Numbers

TL;DR

This paper explores the invariance properties of quadrahyperbolic numbers, revealing a new class of nonlinear transformations that preserve a specific scalar product, thus extending the understanding of their symmetry group.

Contribution

It introduces a novel 3-parametric nonlinear invariance group for the scalar product in quadrahyperbolic numbers, expanding the mathematical framework of these hypercomplex systems.

Findings

Existence of 3-parametric nonlinear invariance transformations

Identification of a scalar product invariant under these transformations

Extension of symmetry group for quadrahyperbolic numbers

Abstract

One may ask whether an extended group of invariance can naturally be attributed to the space of associative commutative Quadrahyperbolic Numbers? To search for a rigorous and positive answer to the question, we shall focus on the method of derivation of the respective invariance. The outcome that there exist 3--parametric nonlinear transformations which leave invariant the scalar product chosen appropriately for The Quadrahyperbolic Numbers, is the main result of the present publication.