English

Constructing zero divisors in the higher dimensional Cayley-Dickson algebras

Rings and Algebras 2007-05-23 v1 Algebraic Topology

Abstract

In this paper we give new methods to construct zero divisors in A_n =R^(2^n) the Cayley_Dickson algebras over the real numbers, for n larger than 4, and we also relate the set of zero divisors in A_{n+1} with the Stiefel Manifold V_{2^n -1,2} for n>3. We also introduce the notion of "Spectrum" (of a no zero double pure element) wich synthesize the information regarding the structure of the linear operators left and right multiplication by the element. We use this as a main technical tool to construct the zero divisors.

Keywords

Cite

@article{arxiv.math/0512517,
  title  = {Constructing zero divisors in the higher dimensional Cayley-Dickson algebras},
  author = {Guillermo Moreno},
  journal= {arXiv preprint arXiv:math/0512517},
  year   = {2007}
}

Comments

28 pages,submmited to Boletin de la Sociedad Matematica Mexicana