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3-Parameter Generalized Quaternions

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 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/s40315-022-00451-7
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Sep 1, 2022

Keywords: 3-Parameter generalized quaternion; Lie algebra; De Moivre’s formula; Matrix representation of quaternions; Euler formula; 14A20; 14A22; 15A66; 70G55; 70G65

References