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May 2016 An Alternate Cayley-Dickson Product
John W. Bales
Missouri J. Math. Sci. 28(1): 88-96 (May 2016). DOI: 10.35834/mjms/1474295358


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.


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John W. Bales. "An Alternate Cayley-Dickson Product." Missouri J. Math. Sci. 28 (1) 88 - 96, May 2016.


Published: May 2016
First available in Project Euclid: 19 September 2016

zbMATH: 06647881
MathSciNet: MR3549810
Digital Object Identifier: 10.35834/mjms/1474295358

Primary: 16S99
Secondary: 16W99

Keywords: Cayley-Dickson , doubling product , Fractal , twist tree , twisted group product

Rights: Copyright © 2016 Central Missouri State University, Department of Mathematics and Computer Science


Vol.28 • No. 1 • May 2016
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