English

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Revised version of 2001 unpublished pre-print