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Volume :14 Issue : 2 1987      Add To Cart                                                                    Download

Cauchy-Riemann conditions for algebras isomorphic to the circulant algebra

Auther : ALAN C. WILDE

Department of Mathematics, University of Michigan, Ann Arbr, Michigan 48109, USA

 

ABSTRACT

 

This paper generalizes the Cauchy-Riemann equations for complex differentiable functions to functions over certain n-dimensional commutative algebras over C with identity. Since the corresponding linear first order partial differential equations depend, u priori, on the basis chosen, this paper shows that in fact the set of functions which are differentiable is independent of the choice of basis. In the process, this paper generalizes to higher dimensions the notions of real and imaginary parts and of conjugation and the relationship between conjugation and multiplication for algebras over C2.

 

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