The Exponential Map on the Cayley-dickson Algebras

We study the Exponential map for A n = R 2 n , the Cayley-Dickson algebras for n ≥ 1, which generalize the complex exponential map to Quater-nions, Octonions and so forth. As an application, we show that the selfmap of the unit sphere in A n , S(A n) = S 2 n −1 , given by taking k-powers has topo-logical degree k for k an integer number, from this we derive… CONTINUE READING