Automorphism groups of Cayley-Dickson loops

2011/02/25 by Jenya Kirshtein, Kirshtein, Jenya
Engineering · Mathematics · #Advanced Materials and Mechanics #Algebraic and Geometric Analysis #FOS: Mathematics #Group Theory (math.GR) #Mathematics and Applications #Rings and Algebras (math.RA) #math.GR #math.RA

paper · pdf · doi:10.48550/arxiv.1102.5151

15 pages

openalex publication_date 2011/02/25 · arxiv created 2012/04/21 · arxiv updated 2012/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Cayley-Dickson loop Q_n is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley-Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, sedenions). We discuss properties of the Cayley-Dickson loops, show that these loops are Hamiltonian, and describe the structure of their automorphism groups.

Related

• Loops with involution and the Cayley-Dickson doubling process
• Multiplication groups and inner mapping groups of Cayley-Dickson loops
• Structure of the Cayley-Dickson algebras
• About some properties of algebras obtained by the Cayley-Dickson process
• The Cayley-Dickson process for dialgebras