Missouri Journal of Mathematical Sciences

An Alternate Cayley-Dickson Product

John W. Bales

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Although the Cayley-Dickson algebras are twisted group algebras, little attention has been paid to the nature of the Cayley-Dickson twist. One reason is that the twist appears to be highly chaotic and there are other interesting things about the algebras to focus attention upon. However, if one uses a doubling product for the algebras different from yet equivalent to the ones commonly used, and if one uses a numbering of the basis vectors different from the standard basis a quite beautiful and highly periodic twist emerges. This leads easily to a simple closed form equation for the product of any two basis vectors of a Cayley-Dickson algebra.

Article information

Missouri J. Math. Sci., Volume 28, Issue 1 (2016), 88-96.

First available in Project Euclid: 19 September 2016

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16S99: None of the above, but in this section
Secondary: 16W99: None of the above, but in this section

Cayley-Dickson doubling product twisted group product fractal twist tree


Bales, John W. An Alternate Cayley-Dickson Product. Missouri J. Math. Sci. 28 (2016), no. 1, 88--96. doi:10.35834/mjms/1474295358. https://projecteuclid.org/euclid.mjms/1474295358

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