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Automorphism groups of Cayley-Dickson loops

By Jenya Kirshtein

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.Comment: 15 page

Topics: Mathematics - Group Theory, Mathematics - Rings and Algebras
Year: 2012
OAI identifier: oai:arXiv.org:1102.5151
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