Automorphism groups of Cayley-Dickson loops

Details Automorphism groups of Cayley-Dickson loops Automorphism groups of Cayley-Dickson loops

2011-02-25

arxiv.org/abs/1102.5151v2

Mathematics

Group Theory

15 pages

Scientific paper

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.

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