Quaternion typification of Clifford algebra elements

TL;DR

This paper introduces a quaternion-based classification system for Clifford algebra elements, enabling new analysis methods for their commutators and anticommutators, and revealing novel properties of these elements.

Contribution

The paper develops a quaternion type classification for Clifford algebra elements, providing a new approach to analyze their algebraic properties and relationships.

Findings

New quaternion type classification for Clifford algebra elements

Method for analyzing commutators and anticommutators

Discovery of new properties of Clifford algebra elements

Abstract

We present a new classification of Clifford algebra elements. Our classification is based on the notion of quaternion type. Using this classification we develop a method for analyzing of commutators and anticommutators of Clifford algebra elements. This method allows us to find out and prove a number of new properties of Clifford algebra elements.