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arXiv · 1602.02317

An alternate Cayley-Dickson product

John Wayland Bales
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Abstract

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 formula for the product of any two basis vectors of a Cayley-Dickson algebra.

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John Wayland Bales. 2016-02-06. An alternate Cayley-Dickson product. https://arxiv.org/abs/1602.02317

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