Constructing zero divisors in the higher dimensional Cayley-Dickson algebras

Details Constructing zero divisors in the higher dimensional Cayley-Dickson algebras Constructing zero divisors in the higher dimensional Cayley-Dickson algebras

2005-12-22

arxiv.org/abs/math/0512517v1

Mathematics

Rings and Algebras

28 pages,submmited to Boletin de la Sociedad Matematica Mexicana

Scientific paper

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.

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