Time-like definition of quaternions in exterior algebra

TL;DR

This paper presents a formal description of quaternions using exterior calculus in a 3D space-time with three time-like coordinates, enabling a consistent quaternion formulation and rotation representation.

Contribution

It introduces a novel quaternion formulation based on exterior algebra in a space-time with three time-like dimensions.

Findings

Successfully recovers quaternion formulation from exterior algebra properties.

Demonstrates how rotations can be expressed using the exterior algebra-based quaternions.

Abstract

A formal description of quaternions by means of exterior calculus is presented. Considering a three-dimensional space-time characterized by three time-like coordinates, we have been able to consistently recover a suitable formulation of quaternions by means of the properties arising from exterior algebra and calculus. As an application, it is also illustrated how rotations may be written in terms of quaternions, in accordance with definition provided in exterior algebra.