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

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  • Ji Eun Kim
  • V. Ravichandran

Abstract

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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  • Ji Eun Kim & V. Ravichandran, 2021. "Characteristics of Regular Functions Defined on a Semicommutative Subalgebra of 4-Dimensional Complex Matrix Algebra," Journal of Mathematics, Hindawi, vol. 2021, pages 1-9, December.
    • Handle: RePEc:hin:jjmath:3163532
    DOI: 10.1155/2021/3163532
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