Alternative elements in the Cayley-Dickson algebras
Rings and Algebras
2007-05-23 v1 Quantum Algebra
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 .
Cite
@article{arxiv.math/0404395,
title = {Alternative elements in the Cayley-Dickson algebras},
author = {Guillermo Moreno},
journal= {arXiv preprint arXiv:math/0404395},
year = {2007}
}
Comments
Revised version of 2001 unpublished pre-print