Characteristics of Regular Functions Defined on a Semicommutative Subalgebra of 4-Dimensional Complex Matrix Algebra

In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂℂ2 of the complex matrix algebra M4,ℂ. We exhibit regular functions defined on a domain in ℂ4 but taking values in ℂℂ2. By using the characteristics of these regula...

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Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2021; pp. 1 - 9
Main Author Kim, Ji Eun
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 2021
John Wiley & Sons, Inc
Wiley
Subjects
Algebra
Investigations
Mathematical analysis
Mathematics
Matrix algebra
Number systems
Quaternions
Variables
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Summary:In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂℂ2 of the complex matrix algebra M4,ℂ. We exhibit regular functions defined on a domain in ℂ4 but taking values in ℂℂ2. By using the characteristics of these regular functions, we propose the corresponding Cauchy–Riemann equations. In addition, we demonstrate several properties of these regular functions using these novel Cauchy–Riemann equations. Mathematical Subject Classification is 32G35, 32W50, 32A99, and 11E88.
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ISSN:2314-4629
2314-4785
DOI:10.1155/2021/3163532