2021/01/28 by Tuncay Deniz Şentürk, Şentürk, Tuncay Deniz, Zafer Ünal +1 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #14A20 #14A22 #15A66 #70G55 #70G65 #Advanced Mathematical Theories and Applications #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2101.11928
openalex publication_date 2021/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we give the most genaral form of the quaternions algebra depending on 3-parameters. We define 3-parameter generalized quaternions (3PGQs) and study on various properties and applications. Firstly we present the definiton, the multiplication table another properties of 3PGQs such as addition-substraction, multiplication and multiplication by scalar operations, unit and inverse elements, conjugate and norm. We give matrix representation and Hamilton operators for 3PGQs. We get polar represenation, De Moivre's and Euler's formulas with the matrix representations for 3PGQs. Besides, we give relations among the powers of the matrices associated with 3PGQs. Finally, Lie group and Lie algebra are studied and their matrix representations are shown. Also the Lie multiplication and the killing bilinear form are given.