Constructing zero divisors in the higher dimensional Cayley-Dickson algebras
环与代数
2007-05-23 v1 代数拓扑
摘要
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.
引用
@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}
}
备注
28 pages,submmited to Boletin de la Sociedad Matematica Mexicana