3-Parameter Generalized Quaternions

In this article, we give a general form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized quaternions (3PGQs) and study various properties and applications. Firstly we present the definiton, the multiplication table and algebraic properties of 3PGQs. We give mat...

Full description

Saved in:
Bibliographic Details
Published in:Computational methods and function theory 2022-09, Vol.22 (3), p.575-608
Main Authors: Şentürk, Tuncay Deniz, Ünal, Zafer
Format: Article
Language:English
Subjects:
Analysis
Computational Mathematics and Numerical Analysis
Functions of a Complex Variable
Group theory
Lie groups
Mathematical tables
Mathematics
Mathematics and Statistics
Matrix algebra
Matrix representation
Multiplication
Operators (mathematics)
Parameters
Quaternions
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this article, we give a general form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized quaternions (3PGQs) and study various properties and applications. Firstly we present the definiton, the multiplication table and algebraic properties of 3PGQs. We give matrix representation and Hamilton operators for 3PGQs. We derive the polar represenation, De Moivre’s and Euler’s formulas with the matrix representations for 3PGQs. Additionally, we derive relations between the powers of the matrices associated with 3PGQs. Finally, Lie groups and Lie algebras are studied and their matrix representations are given. Also the Lie multiplication and the Killing bilinear form are given.
ISSN:1617-9447
2195-3724
DOI:10.1007/s40315-022-00451-7