Computing Characteristics of One Class of Non-commutative Hypercomplex Number Systems of 4-dimension

TL;DR

This paper investigates 4-dimensional non-commutative hypercomplex number systems, providing their construction, algebraic properties, operation algorithms, and exponential function formulas, advancing understanding of their mathematical structure.

Contribution

It systematically constructs all such hypercomplex systems and develops algorithms for their operations and algebraic characteristic calculations.

Findings

All systems in the class are explicitly constructed.

Algorithms for operations in these systems are developed.

Formulas for exponential functions in these systems are provided.

Abstract

The class of non-commutative hypercomplex number systems (HNS) of 4-dimension constructed by using of non-commutative procedure of Grassman-Clifford doubling of 2-dimensional systems is investigated in the article. All HNS of this class are constructed, algorithms of performance of operations and methods of algebraic characteristics calculation in them, such as conjugation, normalization, a type of zero dividers are investigated. Formulas of exponential functions representation in these systems are displayed.