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The Exponential Map on the Cayley-Dickson algebras

Guillermo Moreno
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Abstract

we study the exponential map for A_n = R^2^n, the Cayley_Dickson algebras for n bigher than 1,wich generalize the Complex exponential map to Quaternions,Octonions and so forth. As application,we show that the self-map of the unit sphere in A_n, S^(2^n)-1,given by taking k-powers has topological degree k for k an integer number,from this we derive a suitable "Fundamental theorem of algebra" for A_n for n bigher than 1.

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Guillermo Moreno. 2004-05-21. The Exponential Map on the Cayley-Dickson algebras. https://arxiv.org/abs/math/0405424

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