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Alternative elements in the Cayley-Dickson algebras

Guillermo Moreno
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Abstract

An element a in A_n, the Cayley-Dickson algebra is alternative if (a,a,x)=0 for all x. In this paper we characterise such elements for n>3.To do so,we prove first the so called Yui's conjecture:For a and b pure elements in A_n. If (a,x,b)=0 for all x then a and b are linearly dependent.Also we study alternativity between every two elements and relate this with the norm of their product .

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Guillermo Moreno. 2004-04-21. Alternative elements in the Cayley-Dickson algebras. https://arxiv.org/abs/math/0404395

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