Yayın: 3-Parameter Generalized Quaternions
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Özet
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.
30 pages
30 pages
Açıklama
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Springer Science and Business Media LLC
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Clifford algebras, spinors, A20, 14A22, 15A66, 70G55, 70G65, Mathematics - Algebraic Geometry, Matrices over special rings (quaternions, finite fields, etc.), parameter generalized quaternion, Lie algebra, Euler formula, de Moivre formula, FOS: Mathematics, Quaternion and other division algebras: arithmetic, zeta functions, matrix representation of quaternions, Algebraic Geometry (math.AG)