## Journal of Generalized Lie Theory and Applications

### Automorphism Groups of Cayley-Dickson Loops

Jenya Kirshtein

#### Abstract

The Cayley-Dickson $Q_n$ loop 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, and sedenions).We discuss properties of the Cayley-Dickson loops, show that these loops are Hamiltonian, and describe the structure of their automorphism groups.

#### Article information

Source
J. Gen. Lie Theory Appl., Volume 6 (2012), 15 pages.

Dates
First available in Project Euclid: 15 September 2017

https://projecteuclid.org/euclid.jglta/1505440830

Mathematical Reviews number (MathSciNet)
MR2954624

Zentralblatt MATH identifier
1258.20057

#### Citation

Kirshtein, Jenya. Automorphism Groups of Cayley-Dickson Loops. J. Gen. Lie Theory Appl. 6 (2012), 15 pages. https://projecteuclid.org/euclid.jglta/1505440830