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

2014/12/28 by Yakiv O. Kalinovsky, Kalinovsky, Yakiv O., Yuliya E. Boyarinova +5
Engineering · Mathematics · #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Numerical Analysis (math.NA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1412.8185

openalex publication_date 2014/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The class of non-commutative hypercomplex number systems (HNS) of\n4-dimension, constructed by using of non-commutative Grassmann-Clifford\nprocedure of doubling of 2-dimensional systems is investigated in the article\nand established here are their relationships with the generalized quaternions.\nAlgorithms of performance of operations and methods of algebraic\ncharacteristics calculation in them, such as conjugation, normalization, a type\nof zero divisors are investigated. The considered arithmetic and algebraic\noperations and procedures in this class HNS allow to use these HNS in\nmathematical modeling.\n

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