Generalized quaternions and their relations with Grassmann-Clifford procedure of doubling

TL;DR

This paper explores 4-dimensional non-commutative hypercomplex systems created via Grassmann-Clifford doubling, establishing their connection with generalized quaternions and analyzing their algebraic properties for potential use in mathematical modeling.

Contribution

It introduces a class of 4D hypercomplex systems constructed through Grassmann-Clifford doubling and investigates their algebraic operations and relationships with generalized quaternions.

Findings

Established relationships between these hypercomplex systems and generalized quaternions.

Developed algorithms for algebraic operations and characteristics calculation.

Analyzed properties like conjugation, normalization, and zero divisors.

Abstract

The class of non-commutative hypercomplex number systems (HNS) of 4-dimension, constructed by using of non-commutative Grassmann-Clifford procedure of doubling of 2-dimensional systems is investigated in the article and established here are their relationships with the generalized quaternions. Algorithms of performance of operations and methods of algebraic characteristics calculation in them, such as conjugation, normalization, a type of zero divisors are investigated. The considered arithmetic and algebraic operations and procedures in this class HNS allow to use these HNS in mathematical modeling.