Development of the method of quaternion typification of Clifford algebra elements

TL;DR

This paper advances a quaternion-based classification method for Clifford algebra elements, enabling new insights into their properties through the use of commutators, anticommutators, and elementary functions.

Contribution

It introduces a refined quaternion typification approach for Clifford algebra elements, revealing new algebraic properties and classifications.

Findings

New classification of Clifford algebra elements

Identification of properties using commutators and anticommutators

Analysis of Clifford and exterior degrees and elementary functions

Abstract

In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and prove a number of new properties of Clifford algebra. We use k-fold commutators and anticommutators. In this paper we consider Clifford and exterior degrees and elementary functions of Clifford algebra elements.