The Exponential Map on the Cayley-Dickson algebras
Abstract
we study the exponential map for An = R2n, the CayleyDickson 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 An, S(2n)-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 An for n bigher than 1.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.