Generalized quaternions and their relations with Grassmann-Clifford procedure of doubling
This is an incremental theoretical contribution for mathematicians working on hypercomplex number systems, providing a unified framework but without empirical validation or concrete applications.
The paper investigates 4-dimensional non-commutative hypercomplex number systems constructed via a non-commutative Grassmann-Clifford doubling procedure, establishing their relationships with generalized quaternions. It provides algorithms for operations and algebraic characteristics, enabling their use in mathematical modeling.
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.