The Exponential Map on the Cayley-Dickson algebras

2004/05/21 by Guillermo Moreno, Moreno, Guillermo
Mathematics · #17A99 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic and Geometric Analysis #FOS: Mathematics #Quantum Algebra (math.QA) #advanced mathematical theories #math.AT #math.QA #msc:17A99

paper · pdf · doi:10.48550/arxiv.math/0405424

17 pages

arxiv created 2004/05/21 · openalex publication_date 2004/05/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

we study the exponential map for A_n = R²ⁿ, 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^(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 A_n for n bigher than 1.

Related

• About some properties of algebras obtained by the Cayley-Dickson process
• Automorphism groups of Cayley-Dickson loops
• Some Graded Identities of The Cayley-Dickson Algebra
• The C*-algebra of the exponential function
• Values for the levels and sublevels of algebras obtained by the Cayley-Dickson process