The coquaternion algebra and complex partial differential equations
- Conference date: 7–12 June 2009
- Location: Sozopol (Bulgaria)
In this paper we consider the problem of differentiation of coquaternionic functions. Let us recall that coquaternions are elements of an associative non‐commutative real algebra with zero divisor, introduced by James Cockle (1849) under the name of split‐quaternions or coquaternions. Developing two type complex representations for Cockle algebra (complex and paracomplex ones) we present the problem in a non‐commutative form of the δ̄‐type holomorphy. We prove that corresponding differentiable coquaternionic functions, smooth and analytic, satisfy PDE of complex, and respectively of real variables. Applications for coquaternionic polynomials are sketched.
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